diff --git a/src/ecs/archegraph.rs b/src/ecs/archegraph.rs
new file mode 100644
index 0000000..f62c37c
--- /dev/null
+++ b/src/ecs/archegraph.rs
@@ -0,0 +1,297 @@
+use std::alloc::Layout;
+use std::collections::{HashMap, HashSet};
+
+use super::archetable::{Archetable, EntityRow};
+use super::component::Component;
+use super::entity::Entity;
+use super::prelude::Archetype;
+use super::world::World;
+
+pub struct Archegraph {
+    node_count: usize,
+    node_storage: Vec<Option<Node>>,
+    // unused_indices: Vec<NodeIndex>,
+    type_lookup: HashMap<Archetype, NodeIndex>,
+}
+
+pub type NodeIndex = usize;
+
+pub struct Node {
+    index: NodeIndex,
+    archetable: Archetable,
+    with: HashMap<Component, NodeIndex>,
+    without: HashMap<Component, NodeIndex>,
+}
+
+pub type GraphEntityIndex = super::entity_index::EntityIndex<(NodeIndex, EntityRow)>;
+
+impl Archegraph {
+    pub fn new() -> Self {
+        // Empty archetable is added in `World::bootstrap_archetable`.
+        Self {
+            node_count: 0,
+            node_storage: Vec::new(),
+            // unused_indices: Vec::new(),
+            type_lookup: HashMap::new(),
+        }
+    }
+
+    pub fn bootstrap(&mut self, pairs: Vec<(Entity, Layout)>) {
+        // Inner function is just so call to `bootstrap` is prettier.
+        fn inner(graph: &mut Archegraph, pairs: Vec<(Entity, Layout)>, mut start_index: usize) {
+            // Iterate all the subsets of the pairs and initialize them, first.
+            // The `start_index` should ensure that no subset is bootstrapped twice.
+            for i in start_index..pairs.len() {
+                let mut pairs_subset = pairs.clone();
+                pairs_subset.remove(i);
+                inner(graph, pairs_subset, start_index);
+                start_index += 1;
+            }
+
+            let layouts = pairs.iter().map(|p| Some(p.1)).collect();
+            let archetype = Archetype::new(pairs.iter().map(|p| p.0));
+            let archetable = Archetable::new(archetype, layouts);
+
+            // No entity lookups necessary during bootstrapping.
+            graph.insert(archetable, &GraphEntityIndex::EMPTY);
+        }
+        inner(self, pairs, 0);
+    }
+
+    #[inline]
+    #[must_use]
+    pub fn node_count(&self) -> usize {
+        self.node_count
+    }
+
+    #[must_use]
+    pub fn root(&self) -> &Node {
+        self.node_storage[0].as_ref().unwrap()
+    }
+
+    #[must_use]
+    pub fn root_mut(&mut self) -> &mut Node {
+        self.node_storage[0].as_mut().unwrap()
+    }
+
+    #[must_use]
+    pub fn get(&self, index: NodeIndex) -> Option<&Node> {
+        self.node_storage.get(index).and_then(Option::as_ref)
+    }
+
+    #[must_use]
+    pub fn get_mut(&mut self, index: NodeIndex) -> Option<&mut Node> {
+        self.node_storage.get_mut(index).and_then(Option::as_mut)
+    }
+
+    #[must_use]
+    pub fn lookup_or_create(
+        &mut self,
+        archetype: &Archetype,
+        entity_index: &GraphEntityIndex,
+    ) -> &mut Node {
+        if let Some(index) = self.type_lookup.get(&archetype) {
+            // SAFETY: `type_lookup` is guaranteed to point to a valid archetable.
+            self.node_storage[*index].as_mut().unwrap()
+        } else {
+            let layouts = self.get_layouts(archetype, entity_index);
+            let archetable = Archetable::new(archetype.clone(), layouts);
+            self.insert(archetable, entity_index)
+        }
+    }
+
+    pub fn insert(&mut self, archetable: Archetable, entity_index: &GraphEntityIndex) -> &mut Node {
+        let archetype = archetable.archetype().clone();
+        let index = self.reserve_archetable_index();
+        let mut node = Node::new(index, archetable);
+
+        self.type_lookup.insert(archetype, index);
+        self.fill_edges(&mut node, entity_index);
+
+        let entry = &mut self.node_storage[index];
+        *entry = Some(node);
+        entry.as_mut().unwrap()
+    }
+
+    fn get_layout(&self, component: Component, entity_index: &GraphEntityIndex) -> Option<Layout> {
+        // FIXME: Relations can be components too.
+        let entity: Entity = component.try_into().ok()?;
+        let (node_index, row) = entity_index.get(entity.id())?.data;
+        let archetable = self.get(node_index).unwrap().get();
+        let component_index = archetable.archetype().position(World::LAYOUT)?;
+        let column = archetable.column_by_index(component_index).unwrap();
+        let column = unsafe { column.as_typed_slice::<Layout>() };
+        Some(column[row])
+    }
+
+    fn get_layouts(
+        &self,
+        archetype: &Archetype,
+        entity_index: &GraphEntityIndex,
+    ) -> Vec<Option<Layout>> {
+        let iter = archetype.components().iter();
+        iter.map(|c| self.get_layout(*c, entity_index)).collect()
+    }
+
+    #[must_use]
+    fn reserve_archetable_index(&mut self) -> usize {
+        self.node_count += 1;
+        // self.unused_indices.pop().unwrap_or_else(|| {
+        self.node_storage.push(None);
+        self.node_storage.len() - 1
+        // })
+    }
+
+    fn fill_edges(&mut self, node: &mut Node, entity_index: &GraphEntityIndex) {
+        let archetype = node.archetable.archetype();
+        for component in archetype.components() {
+            let other_archetype = archetype.clone().without(*component);
+            let other_node = self.lookup_or_create(&other_archetype, entity_index);
+            node.without.insert(*component, other_node.index);
+            other_node.with.insert(*component, node.index);
+        }
+    }
+}
+
+impl Node {
+    #[must_use]
+    fn new(index: NodeIndex, archetable: Archetable) -> Self {
+        Self {
+            index,
+            archetable,
+            with: HashMap::new(),
+            without: HashMap::new(),
+        }
+    }
+
+    #[inline]
+    #[must_use]
+    pub fn index(&self) -> NodeIndex {
+        self.index
+    }
+
+    #[inline]
+    #[must_use]
+    pub fn get(&self) -> &Archetable {
+        &self.archetable
+    }
+
+    #[inline]
+    #[must_use]
+    pub fn get_mut(&mut self) -> &mut Archetable {
+        &mut self.archetable
+    }
+
+    #[inline]
+    #[must_use]
+    pub fn iter<'a>(&self, archegraph: &'a Archegraph) -> impl Iterator<Item = &'a Archetable> {
+        GraphIter::new(archegraph, self.index)
+    }
+}
+
+struct GraphIter<'a> {
+    archegraph: &'a Archegraph,
+    stack: Vec<NodeIndex>,
+    visited: HashSet<NodeIndex>,
+}
+
+impl GraphIter<'_> {
+    fn new(archegraph: &Archegraph, start_index: NodeIndex) -> GraphIter {
+        GraphIter {
+            archegraph,
+            stack: vec![start_index],
+            visited: HashSet::new(),
+        }
+    }
+}
+
+impl<'a> Iterator for GraphIter<'a> {
+    type Item = &'a Archetable;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        while let Some(index) = self.stack.pop() {
+            if !self.visited.contains(&index) {
+                let node = self.archegraph.get(index).unwrap();
+                self.stack.extend(node.with.values());
+                self.visited.insert(index);
+                return Some(&node.archetable);
+            }
+        }
+        None
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn bootstrap() {
+        let mut archegraph = Archegraph::new();
+
+        let a = Entity::new_checked(1, 0).unwrap();
+        let b = Entity::new_checked(2, 0).unwrap();
+        let c = Entity::new_checked(10, 0).unwrap();
+        let d = Entity::new_checked(2000, 0).unwrap();
+
+        archegraph.bootstrap(vec![
+            (a, Layout::new::<u8>()),
+            (b, Layout::new::<u16>()),
+            (c, Layout::new::<u32>()),
+            (d, Layout::new::<u64>()),
+        ]);
+
+        // {a, b, c, d} has 16 subsets including {} (the empty root archetype)
+        // and {a, b, c, d} (archetype containing all components at the same time).
+        assert_eq!(16, archegraph.node_count());
+
+        let mut archetypes = archegraph
+            .root()
+            .iter(&archegraph)
+            .map(Archetable::archetype)
+            .map(Archetype::components)
+            .collect::<Vec<_>>();
+
+        // Not guaranteed to iter in any specific order.
+        archetypes.sort();
+
+        assert_eq!(
+            vec![
+                vec![],
+                vec![a],
+                vec![a, b],
+                vec![a, b, c],
+                vec![a, b, c, d],
+                vec![a, b, d],
+                vec![a, c],
+                vec![a, c, d],
+                vec![a, d],
+                vec![b],
+                vec![b, c],
+                vec![b, c, d],
+                vec![b, d],
+                vec![c],
+                vec![c, d],
+                vec![d],
+            ],
+            archetypes
+        );
+
+        // Ensure the columns' layouts are correct for a given Archetype.
+        let archetype = Archetype::new([a, c, d]);
+        let index = &GraphEntityIndex::EMPTY;
+        let table = &archegraph.lookup_or_create(&archetype, index).get();
+        assert_eq!(
+            Layout::new::<u8>(),
+            table.column_by_index(0).unwrap().layout()
+        );
+        assert_eq!(
+            Layout::new::<u32>(),
+            table.column_by_index(1).unwrap().layout()
+        );
+        assert_eq!(
+            Layout::new::<u64>(),
+            table.column_by_index(2).unwrap().layout()
+        );
+    }
+}
diff --git a/src/ecs/archetable.rs b/src/ecs/archetable.rs
index 53ea9db..9418c3d 100644
--- a/src/ecs/archetable.rs
+++ b/src/ecs/archetable.rs
@@ -1,54 +1,44 @@
-use std::any::TypeId;
+use std::alloc::Layout;
 
 use super::archetype::Archetype;
 use super::entity::Entity;
-use super::world::World;
-
+use super::prelude::Component;
 use super::utility::RawComponentVec;
 
 pub struct Archetable {
     archetype: Archetype,
-    components: Vec<ComponentInfo>,
-    columns: Vec<Column>,
+    components: Vec<ComponentData>,
+    columns: Vec<ColumnData>,
     entities: Vec<Entity>,
 }
 
+/// Represents an index into the `entities` vector of an `Archetable`.
 pub type EntityRow = usize;
 
-struct ComponentInfo {
-    entity: Entity,
-    type_id: Option<TypeId>,
-    column_index: Option<usize>,
+/// Represents an index into the `columns` vector of an `Archetable`.
+pub type ValueComponentColumn = usize;
+
+pub struct ComponentData {
+    column_index: Option<ValueComponentColumn>,
 }
 
-struct Column {
+struct ColumnData {
     data: RawComponentVec,
     component_index: usize,
 }
 
 impl Archetable {
     #[must_use]
-    pub fn new_empty() -> Self {
-        Self {
-            archetype: Archetype::EMPTY,
-            components: Vec::new(),
-            columns: Vec::new(),
-            entities: Vec::new(),
-        }
-    }
+    pub fn new(archetype: Archetype, layouts: Vec<Option<Layout>>) -> Self {
+        assert_eq!(archetype.components().len(), layouts.len());
 
-    #[must_use]
-    pub fn new(world: &World, archetype: Archetype) -> Self {
         let mut components = Vec::new();
         let mut columns = Vec::new();
 
-        for component in archetype.components() {
-            let entity = (*component).try_into().unwrap();
-            let (layout, type_id) = world.lookup_component_info(entity).unzip();
-
+        for layout in layouts {
             // If the entity has `Layout`, add a column for it.
             let column_index = if let Some(layout) = layout {
-                columns.push(Column {
+                columns.push(ColumnData {
                     data: RawComponentVec::new(layout),
                     component_index: components.len(),
                 });
@@ -57,11 +47,7 @@ impl Archetable {
                 None
             };
 
-            components.push(ComponentInfo {
-                entity,
-                column_index,
-                type_id,
-            });
+            components.push(ComponentData { column_index });
         }
 
         Self {
@@ -72,7 +58,13 @@ impl Archetable {
         }
     }
 
-    pub fn push(&mut self, entity: Entity) -> EntityRow {
+    #[inline]
+    #[must_use]
+    pub fn archetype(&self) -> &Archetype {
+        &self.archetype
+    }
+
+    pub fn insert(&mut self, entity: Entity) -> EntityRow {
         self.entities.push(entity);
         let new_len = self.entities.len();
         for column in self.columns.iter_mut() {
@@ -92,23 +84,33 @@ impl Archetable {
         self.entities.get(row).copied()
     }
 
-    fn find_component_info<T: 'static>(&self) -> Option<&ComponentInfo> {
-        let type_id = Some(TypeId::of::<T>());
-        self.components.iter().find(|e| e.type_id == type_id)
+    #[must_use]
+    pub fn column_by_index(&self, index: ValueComponentColumn) -> Option<&RawComponentVec> {
+        Some(&self.columns.get(index)?.data)
+    }
+
+    #[must_use]
+    pub fn column_by_index_mut(
+        &mut self,
+        index: ValueComponentColumn,
+    ) -> Option<&mut RawComponentVec> {
+        Some(&mut self.columns.get_mut(index)?.data)
     }
 
     #[must_use]
-    pub fn get_component_column<T: 'static>(&self) -> Option<&[T]> {
-        let info = self.find_component_info::<T>()?;
-        let column = &self.columns[info.column_index?];
-        Some(unsafe { column.data.as_typed_slice::<T>() })
+    pub fn column_by_component(&self, component: impl Into<Component>) -> Option<&RawComponentVec> {
+        let component_index = self.archetype.position(component.into())?;
+        let column_index = self.components[component_index].column_index?;
+        self.column_by_index(column_index)
     }
 
     #[must_use]
-    pub fn get_component_column_mut<T: 'static>(&mut self) -> Option<&mut [T]> {
-        let info = self.find_component_info::<T>()?;
-        let column_index = info.column_index?; // Avoid borrow.
-        let column = &mut self.columns[column_index];
-        Some(unsafe { column.data.as_typed_slice_mut::<T>() })
+    pub fn column_by_component_mut(
+        &mut self,
+        component: impl Into<Component>,
+    ) -> Option<&mut RawComponentVec> {
+        let component_index = self.archetype.position(component.into())?;
+        let column_index = self.components[component_index].column_index?;
+        self.column_by_index_mut(column_index)
     }
 }
diff --git a/src/ecs/archetype.rs b/src/ecs/archetype.rs
index fdebfb5..e792aab 100644
--- a/src/ecs/archetype.rs
+++ b/src/ecs/archetype.rs
@@ -1,9 +1,9 @@
 use super::component::Component;
 
-/// Represents a set of components an [`Entity`] may have.
+/// Represents a sorted set of components an [`Entity`] may have.
 ///
 /// [`Entity`]: super::entity::Entity
-#[derive(Clone, Eq, PartialEq, Ord, PartialOrd, Hash)]
+#[derive(Clone, Eq, PartialEq, Ord, PartialOrd, Hash, Debug)]
 pub struct Archetype {
     components: Vec<Component>,
 }
@@ -15,8 +15,8 @@ impl Archetype {
 
     #[must_use]
     pub fn new(iter: impl IntoIterator<Item = impl Into<Component>>) -> Self {
-        let iter = iter.into_iter().map(Into::into).collect();
-        let mut components: Vec<_> = iter;
+        let iter = iter.into_iter().map(Into::into);
+        let mut components: Vec<_> = iter.collect();
         components.sort();
         components.dedup();
         Self { components }
@@ -33,6 +33,11 @@ impl Archetype {
         self.components.binary_search(&component.into()).is_ok()
     }
 
+    #[must_use]
+    pub fn position(&self, component: impl Into<Component>) -> Option<usize> {
+        self.components.binary_search(&component.into()).ok()
+    }
+
     pub fn add(&mut self, component: impl Into<Component>) {
         let component = component.into();
         if let Err(index) = self.components.binary_search(&component) {
@@ -60,6 +65,12 @@ impl Archetype {
         self.remove(component);
         self
     }
+
+    #[inline]
+    #[must_use]
+    pub fn iter(&self) -> std::slice::Iter<'_, Component> {
+        self.components.iter()
+    }
 }
 
 impl<T> FromIterator<T> for Archetype
@@ -76,7 +87,6 @@ impl IntoIterator for Archetype {
     type Item = Component;
     type IntoIter = std::vec::IntoIter<Self::Item>;
 
-    #[inline]
     fn into_iter(self) -> Self::IntoIter {
         self.components.into_iter()
     }
diff --git a/src/ecs/mod.rs b/src/ecs/mod.rs
index 925fd7b..e849728 100644
--- a/src/ecs/mod.rs
+++ b/src/ecs/mod.rs
@@ -1,3 +1,4 @@
+pub mod archegraph;
 pub mod archetable;
 pub mod archetype;
 pub mod component;
diff --git a/src/ecs/world.rs b/src/ecs/world.rs
index 3f8677a..7f00fe2 100644
--- a/src/ecs/world.rs
+++ b/src/ecs/world.rs
@@ -2,28 +2,35 @@ use std::alloc::Layout;
 use std::any::TypeId;
 use std::collections::HashMap;
 
-use super::archetable::Archetable;
+use crate::ecs::prelude::Archetype;
+
+use super::archegraph::{Archegraph, GraphEntityIndex};
 use super::entity::{Entity, EntityId};
 use super::entity_index::EntityIndex;
 
 pub struct World {
-    entity_index: EntityIndex<usize>,
-    empty_archetable: Archetable,
-    type_id_lookup: HashMap<TypeId, Entity>,
-    // Temporary. To be removed once we can build and use Archetables that hold this information.
-    component_lookup: HashMap<Entity, (Layout, TypeId)>,
+    entity_index: GraphEntityIndex,
+    archegraph: Archegraph,
+    typeid_lookup: HashMap<TypeId, Entity>,
 }
 
 impl World {
+    pub const LAYOUT: Entity = unsafe { Entity::new_unchecked(1, 0) };
+    pub const TYPEID: Entity = unsafe { Entity::new_unchecked(2, 0) };
+
     #[must_use]
     pub fn new() -> Self {
         let mut world = Self {
             entity_index: EntityIndex::new(),
-            empty_archetable: Archetable::new_empty(),
-            type_id_lookup: HashMap::new(),
-            component_lookup: HashMap::new(),
+            archegraph: Archegraph::new(),
+            typeid_lookup: HashMap::new(),
         };
 
+        world.archegraph.bootstrap(vec![
+            (World::LAYOUT, Layout::new::<Layout>()),
+            (World::TYPEID, Layout::new::<TypeId>()),
+        ]);
+
         world.register_component::<Layout>();
         world.register_component::<TypeId>();
 
@@ -37,34 +44,58 @@ impl World {
 
     #[must_use]
     pub fn lookup_by_type<T: 'static>(&self) -> Option<Entity> {
-        self.type_id_lookup.get(&TypeId::of::<T>()).copied()
-    }
-
-    #[must_use]
-    pub fn lookup_component_info(&self, entity: Entity) -> Option<(Layout, TypeId)> {
-        self.component_lookup.get(&entity).copied()
+        self.typeid_lookup.get(&TypeId::of::<T>()).copied()
     }
 
     pub fn register_component<T: 'static>(&mut self) -> Entity {
-        assert_ne!(0, size_of::<T>());
-        let entity = self.create();
-        let component_info = (Layout::new::<T>(), TypeId::of::<T>());
-        self.component_lookup.insert(entity, component_info);
+        let entity = if size_of::<T>() > 0 {
+            let archetype = Archetype::new([Self::LAYOUT, Self::TYPEID]);
+            let entity = self.create(&archetype);
+            entity
+        } else {
+            let archetype = Archetype::new([Self::TYPEID]);
+            let entity = self.create(&archetype);
+            entity
+        };
+
+        let (node_index, row) = self.entity_index.get(entity.id()).unwrap().data;
+        let archetable = self.archegraph.get_mut(node_index).unwrap().get_mut();
+
+        if size_of::<T>() > 0 {
+            let layout_column = archetable.column_by_component_mut(World::LAYOUT).unwrap();
+            let layout_column = unsafe { layout_column.as_typed_slice_mut::<Layout>() };
+            layout_column[row] = Layout::new::<T>();
+        }
+
+        let typeid = TypeId::of::<T>();
+        self.typeid_lookup.insert(typeid, entity);
+
+        let typeid_column = archetable.column_by_component_mut(World::TYPEID).unwrap();
+        let typeid_column = unsafe { typeid_column.as_typed_slice_mut::<TypeId>() };
+        typeid_column[row] = typeid;
+
         entity
     }
 
-    #[must_use]
-    pub fn create(&mut self) -> Entity {
+    pub fn create(&mut self, archetype: &Archetype) -> Entity {
+        let entities = &self.entity_index;
+        let graph_node = self.archegraph.lookup_or_create(archetype, entities);
+        let archetable = graph_node.get_mut();
+
         let entry = self.entity_index.create();
-        let row = self.empty_archetable.push(entry.entity);
-        entry.update(row)
+        let row = archetable.insert(entry.entity);
+
+        entry.update((graph_node.index(), row))
     }
 
     pub fn destroy(&mut self, entity: Entity) -> bool {
-        if let Ok(row) = self.entity_index.destroy(entity) {
-            if let Some(swapped) = self.empty_archetable.swap_remove(row) {
+        if let Ok((node_index, row)) = self.entity_index.destroy(entity) {
+            let graph_node = self.archegraph.get_mut(node_index).unwrap();
+            let archetable = graph_node.get_mut();
+            if let Some(swapped) = archetable.swap_remove(row) {
                 // Assume that `swapped` we got from the archetype table is alive.
-                self.entity_index.get(swapped.id()).unwrap().data = row;
+                let mut entry = self.entity_index.get(swapped.id()).unwrap();
+                entry.data = (graph_node.index(), row);
             }
             true
         } else {
@@ -72,3 +103,23 @@ impl World {
         }
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn world_new_check() {
+        let world = World::new();
+        let (node_index, row) = world.entity_index.get(World::LAYOUT.id()).unwrap().data;
+        let archetable = world.archegraph.get(node_index).unwrap().get();
+
+        let layout_column = archetable.column_by_component(World::LAYOUT).unwrap();
+        let layout_column = unsafe { layout_column.as_typed_slice::<Layout>() };
+        assert_eq!(Layout::new::<Layout>(), layout_column[row]);
+
+        let typeid_column = archetable.column_by_component(World::TYPEID).unwrap();
+        let typeid_column = unsafe { typeid_column.as_typed_slice::<TypeId>() };
+        assert_eq!(TypeId::of::<Layout>(), typeid_column[row]);
+    }
+}