diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7e703f8..d2b298b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -22,6 +22,7 @@ The format is based on [Keep a Changelog], and this project adheres to
   the keys of `iter.Seq2` sequences.
 - Added `sets.NewFromValues()` (and variants) which construct set types from
   the values of `iter.Seq2` sequences.
+- Added `Intersection()` method to all set types.
 
 ### Changed
 
diff --git a/collections/maps/map.go b/collections/maps/map.go
index f2de2e6..d2cf051 100644
--- a/collections/maps/map.go
+++ b/collections/maps/map.go
@@ -110,13 +110,13 @@ func (m *Map[K, V]) TryGet(k K) (V, bool) {
 
 // Clone returns a shallow copy of the map.
 func (m *Map[K, V]) Clone() *Map[K, V] {
-	var x Map[K, V]
+	var out Map[K, V]
 
 	if m != nil {
-		x.elements = maps.Clone(m.elements)
+		out.elements = maps.Clone(m.elements)
 	}
 
-	return &x
+	return &out
 }
 
 // Merge returns a new map containing all key/value pairs from s and x.
@@ -145,34 +145,34 @@ func (m *Map[K, V]) Merge(x *Map[K, V]) *Map[K, V] {
 // Select returns a new map containing all key/value pairs from m for which the
 // given predicate returns true.
 func (m *Map[K, V]) Select(pred func(K, V) bool) *Map[K, V] {
-	var x Map[K, V]
+	var out Map[K, V]
 
 	if m != nil {
 		for k, v := range m.elements {
 			if pred(k, v) {
-				x.Set(k, v)
+				out.Set(k, v)
 			}
 		}
 	}
 
-	return &x
+	return &out
 }
 
 // Project constructs a new map by applying the given transform function to each
 // key/value pair in the map. If the transform function returns false, the key
 // is omitted from the resulting map.
 func (m *Map[K, V]) Project(transform func(K, V) (K, V, bool)) *Map[K, V] {
-	var x Map[K, V]
+	var out Map[K, V]
 
 	if m != nil {
 		for k, v := range m.elements {
 			if k, v, ok := transform(k, v); ok {
-				x.Set(k, v)
+				out.Set(k, v)
 			}
 		}
 	}
 
-	return &x
+	return &out
 }
 
 // All returns a sequence that yields all key/value pairs in the map in no
diff --git a/collections/maps/orderedimpl.go b/collections/maps/orderedimpl.go
index 56cf34a..7ba1509 100644
--- a/collections/maps/orderedimpl.go
+++ b/collections/maps/orderedimpl.go
@@ -238,17 +238,17 @@ func orderedProject[K, V any, M ordered[K, V, I], I any](
 	m M,
 	transform func(K, V) (K, V, bool),
 ) M {
-	var x M = m.new(nil)
+	var out M = m.new(nil)
 
 	if m != nil {
 		for _, pair := range *m.ptr() {
 			if k, v, ok := transform(pair.Key, pair.Value); ok {
-				orderedSet(x, k, v)
+				orderedSet(out, k, v)
 			}
 		}
 	}
 
-	return x
+	return out
 }
 
 func orderedAll[K, V any, M ordered[K, V, I], I any](
diff --git a/collections/maps/proto.go b/collections/maps/proto.go
index b50c00b..0011e9c 100644
--- a/collections/maps/proto.go
+++ b/collections/maps/proto.go
@@ -114,13 +114,13 @@ func (m *Proto[K, V]) TryGet(k K) (V, bool) {
 
 // Clone returns a shallow copy of the map.
 func (m *Proto[K, V]) Clone() *Proto[K, V] {
-	var x Proto[K, V]
+	var out Proto[K, V]
 
 	if m != nil {
-		x.elements = *m.elements.Clone()
+		out.elements = *m.elements.Clone()
 	}
 
-	return &x
+	return &out
 }
 
 // Merge returns a new map containing all key/value pairs from s and x.
@@ -143,27 +143,27 @@ func (m *Proto[K, V]) Merge(x *Proto[K, V]) *Proto[K, V] {
 // Select returns a new map containing all key/value pairs from m for which the
 // given predicate returns true.
 func (m *Proto[K, V]) Select(pred func(K, V) bool) *Proto[K, V] {
-	var x Proto[K, V]
+	var out Proto[K, V]
 
 	if m != nil {
-		x.elements = *m.elements.Select(
+		out.elements = *m.elements.Select(
 			func(s string, v V) bool {
 				return pred(m.unmarshal(s), v)
 			},
 		)
 	}
 
-	return &x
+	return &out
 }
 
 // Project constructs a new map by applying the given transform function to each
 // key/value pair in the map. If the transform function returns false, the key
 // is omitted from the resulting map.
 func (m *Proto[K, V]) Project(transform func(K, V) (K, V, bool)) *Proto[K, V] {
-	var x Proto[K, V]
+	var out Proto[K, V]
 
 	if m != nil {
-		x.elements = *m.elements.Project(
+		out.elements = *m.elements.Project(
 			func(k string, v V) (string, V, bool) {
 				if k, v, ok := transform(m.unmarshal(k), v); ok {
 					return m.marshal(k), v, true
@@ -173,7 +173,7 @@ func (m *Proto[K, V]) Project(transform func(K, V) (K, V, bool)) *Proto[K, V] {
 		)
 	}
 
-	return &x
+	return &out
 }
 
 // All returns a sequence that yields all key/value pairs in the map in no
diff --git a/collections/sets/contract_test.go b/collections/sets/contract_test.go
index 4a89265..145d3f1 100644
--- a/collections/sets/contract_test.go
+++ b/collections/sets/contract_test.go
@@ -24,6 +24,7 @@ type contract[T, I any] interface {
 
 	Clone() *I
 	Union(*I) *I
+	Intersection(*I) *I
 	Select(func(T) bool) *I
 
 	All() iter.Seq[T]
@@ -334,6 +335,40 @@ func testSet[
 						t.Fatal("the result of a union should never be nil")
 					}
 				},
+				"intersection with an overlapping set": func(t *rapid.T) {
+					s := newDisjointSet(t, 0, 3)
+
+					m := drawMember(t)
+					s.Add(m)
+
+					expected = []T{m}
+					subject = subject.Intersection(s)
+					if subject == nil {
+						t.Fatal("the result of an intersection should never be nil")
+					}
+				},
+				"intersection with disjoint set": func(t *rapid.T) {
+					s := newDisjointSet(t, 0, 3)
+
+					expected = nil
+					subject = subject.Intersection(s)
+					if subject == nil {
+						t.Fatal("the result of an intersection should never be nil")
+					}
+				},
+				"interesection with itself": func(t *rapid.T) {
+					subject = subject.Intersection(subject)
+					if subject == nil {
+						t.Fatal("the result of an intersection should never be nil")
+					}
+				},
+				"intersection with a nil set": func(t *rapid.T) {
+					expected = nil
+					subject = subject.Intersection(nil)
+					if subject == nil {
+						t.Fatal("the result of an intersection should never be nil")
+					}
+				},
 				"select a subset": func(t *rapid.T) {
 					subject = subject.Select(
 						func(m T) bool {
diff --git a/collections/sets/ordered.go b/collections/sets/ordered.go
index 5e08cb4..80d6e97 100644
--- a/collections/sets/ordered.go
+++ b/collections/sets/ordered.go
@@ -95,6 +95,11 @@ func (s *Ordered[T]) Union(x *Ordered[T]) *Ordered[T] {
 	return orderedUnion[T](s, x)
 }
 
+// Intersection returns a set containing members that are in both s and x.
+func (s *Ordered[T]) Intersection(x *Ordered[T]) *Ordered[T] {
+	return orderedIntersection[T](s, x)
+}
+
 // Select returns the subset of s containing members for which the given
 // predicate function returns true.
 func (s *Ordered[T]) Select(pred func(T) bool) *Ordered[T] {
diff --git a/collections/sets/orderedbycomparator.go b/collections/sets/orderedbycomparator.go
index e58faff..6fa65a8 100644
--- a/collections/sets/orderedbycomparator.go
+++ b/collections/sets/orderedbycomparator.go
@@ -142,6 +142,11 @@ func (s *OrderedByComparator[T, C]) Union(x *OrderedByComparator[T, C]) *Ordered
 	return orderedUnion[T](s, x)
 }
 
+// Intersection returns a set containing members that are in both s and x.
+func (s *OrderedByComparator[T, C]) Intersection(x *OrderedByComparator[T, C]) *OrderedByComparator[T, C] {
+	return orderedIntersection[T](s, x)
+}
+
 // Select returns the subset of s containing members for which the given
 // predicate function returns true.
 func (s *OrderedByComparator[T, C]) Select(pred func(T) bool) *OrderedByComparator[T, C] {
diff --git a/collections/sets/orderedbymember.go b/collections/sets/orderedbymember.go
index e09be20..b2c2931 100644
--- a/collections/sets/orderedbymember.go
+++ b/collections/sets/orderedbymember.go
@@ -97,6 +97,11 @@ func (s *OrderedByMember[T]) Union(x *OrderedByMember[T]) *OrderedByMember[T] {
 	return orderedUnion[T](s, x)
 }
 
+// Intersection returns a set containing members that are in both s and x.
+func (s *OrderedByMember[T]) Intersection(x *OrderedByMember[T]) *OrderedByMember[T] {
+	return orderedIntersection[T](s, x)
+}
+
 // Select returns the subset of s containing members for which the given
 // predicate function returns true.
 func (s *OrderedByMember[T]) Select(pred func(T) bool) *OrderedByMember[T] {
diff --git a/collections/sets/orderedimpl.go b/collections/sets/orderedimpl.go
index cba9899..118a1a6 100644
--- a/collections/sets/orderedimpl.go
+++ b/collections/sets/orderedimpl.go
@@ -234,16 +234,15 @@ func orderedClone[T any, S ordered[T, I], I any](
 func orderedUnion[T any, S ordered[T, I], I any](
 	x, y S,
 ) S {
-	var membersX, membersY []T
-
-	if x != nil {
-		membersX = *x.ptr()
+	if x == nil {
+		return orderedClone[T](y)
 	}
 
-	if y != nil {
-		membersY = *y.ptr()
+	if y == nil {
+		return orderedClone[T](x)
 	}
 
+	membersX, membersY := *x.ptr(), *y.ptr()
 	indexX, indexY := 0, 0
 	lenX, lenY := len(membersX), len(membersY)
 
@@ -289,6 +288,41 @@ func orderedUnion[T any, S ordered[T, I], I any](
 	return x.new(members)
 }
 
+func orderedIntersection[T any, S ordered[T, I], I any](
+	x, y S,
+) S {
+	if x == nil || y == nil {
+		return x.new(nil)
+	}
+
+	big, small := *x.ptr(), *y.ptr()
+	if len(small) > len(big) {
+		big, small = small, big
+	}
+
+	if len(small) == 0 {
+		return x.new(nil)
+	}
+
+	members := make([]T, 0, len(small))
+
+	for _, m := range small {
+		if len(big) == 0 {
+			break
+		}
+
+		i, ok := slices.BinarySearchFunc(big, m, x.cmp)
+		if ok {
+			members = append(members, m)
+			big = big[i+1:]
+		} else {
+			big = big[i:]
+		}
+	}
+
+	return x.new(members)
+}
+
 func orderedSelect[T any, S ordered[T, I], I any](
 	s S,
 	pred func(T) bool,
diff --git a/collections/sets/proto.go b/collections/sets/proto.go
index 1e36b69..0fd9d61 100644
--- a/collections/sets/proto.go
+++ b/collections/sets/proto.go
@@ -163,13 +163,13 @@ func (s *Proto[T]) IsStrictSubset(x *Proto[T]) bool {
 
 // Clone returns a shallow copy of the set.
 func (s *Proto[T]) Clone() *Proto[T] {
-	var x Proto[T]
+	var out Proto[T]
 
 	if s != nil {
-		x.members = *s.members.Clone()
+		out.members = *s.members.Clone()
 	}
 
-	return &x
+	return &out
 }
 
 // Union returns a set containing all members of s and x.
@@ -187,18 +187,29 @@ func (s *Proto[T]) Union(x *Proto[T]) *Proto[T] {
 	}
 }
 
+// Intersection returns a set containing members that are in both s and x.
+func (s *Proto[T]) Intersection(x *Proto[T]) *Proto[T] {
+	var out Proto[T]
+
+	if s != nil && x != nil {
+		out.members = *s.members.Intersection(&x.members)
+	}
+
+	return &out
+}
+
 // Select returns the subset of s containing members for which the given
 // predicate function returns true.
 func (s *Proto[T]) Select(pred func(T) bool) *Proto[T] {
-	var x Proto[T]
+	var out Proto[T]
 
 	if s != nil {
-		x.members = *s.members.Select(func(m string) bool {
+		out.members = *s.members.Select(func(m string) bool {
 			return pred(s.unmarshal(m))
 		})
 	}
 
-	return &x
+	return &out
 }
 
 // All returns a sequence that yields all members of the set in no particular
diff --git a/collections/sets/set.go b/collections/sets/set.go
index b727036..ae6e635 100644
--- a/collections/sets/set.go
+++ b/collections/sets/set.go
@@ -167,13 +167,13 @@ func (s *Set[T]) IsStrictSubset(x *Set[T]) bool {
 
 // Clone returns a shallow copy of the set.
 func (s *Set[T]) Clone() *Set[T] {
-	var x Set[T]
+	var out Set[T]
 
 	if s != nil {
-		x.members = maps.Clone(s.members)
+		out.members = maps.Clone(s.members)
 	}
 
-	return &x
+	return &out
 }
 
 // Union returns a set containing all members of s and x.
@@ -202,20 +202,44 @@ func (s *Set[T]) Union(x *Set[T]) *Set[T] {
 	}
 }
 
+// Intersection returns a set containing members that are in both s and x.
+func (s *Set[T]) Intersection(x *Set[T]) *Set[T] {
+	if s == nil || x == nil {
+		return &Set[T]{}
+	}
+
+	big, small := s.members, x.members
+	if len(small) > len(big) {
+		big, small = small, big
+	}
+
+	members := make(map[T]struct{}, len(small))
+
+	for m := range small {
+		if _, ok := big[m]; ok {
+			members[m] = struct{}{}
+		}
+	}
+
+	return &Set[T]{
+		members: members,
+	}
+}
+
 // Select returns the subset of s containing members for which the given
 // predicate function returns true.
 func (s *Set[T]) Select(pred func(T) bool) *Set[T] {
-	var x Set[T]
+	var out Set[T]
 
 	if s != nil {
 		for m := range s.members {
 			if pred(m) {
-				x.Add(m)
+				out.Add(m)
 			}
 		}
 	}
 
-	return &x
+	return &out
 }
 
 // All returns a sequence that yields all members of the set in no particular