diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
index 1e0453f08..bfb4199a3 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/AlgebraExtensions.kt
@@ -3,6 +3,8 @@ package scientifik.kmath.operations
 fun <T> Space<T>.sum(data: Iterable<T>): T = data.fold(zero) { left, right -> add(left, right) }
 fun <T> Space<T>.sum(data: Sequence<T>): T = data.fold(zero) { left, right -> add(left, right) }
 
+fun <T : Any, S : Space<T>> Iterable<T>.sumWith(space: S): T = space.sum(this)
+
 //TODO optimized power operation
 fun <T> RingOperations<T>.power(arg: T, power: Int): T {
     var res = arg
diff --git a/kmath-geometry/build.gradle.kts b/kmath-geometry/build.gradle.kts
new file mode 100644
index 000000000..39aa833ad
--- /dev/null
+++ b/kmath-geometry/build.gradle.kts
@@ -0,0 +1,9 @@
+plugins {
+    id("scientifik.mpp")
+}
+
+kotlin.sourceSets.commonMain {
+    dependencies {
+        api(project(":kmath-core"))
+    }
+}
\ No newline at end of file
diff --git a/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Euclidean2DSpace.kt b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Euclidean2DSpace.kt
new file mode 100644
index 000000000..2313b2170
--- /dev/null
+++ b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Euclidean2DSpace.kt
@@ -0,0 +1,58 @@
+package scientifik.kmath.geometry
+
+import scientifik.kmath.linear.Point
+import scientifik.kmath.operations.SpaceElement
+import scientifik.kmath.operations.invoke
+import kotlin.math.sqrt
+
+
+interface Vector2D : Point<Double>, Vector, SpaceElement<Vector2D, Vector2D, Euclidean2DSpace> {
+    val x: Double
+    val y: Double
+
+    override val size: Int get() = 2
+
+    override fun get(index: Int): Double = when (index) {
+        1 -> x
+        2 -> y
+        else -> error("Accessing outside of point bounds")
+    }
+
+    override fun iterator(): Iterator<Double> = listOf(x, y).iterator()
+
+    override val context: Euclidean2DSpace get() = Euclidean2DSpace
+
+    override fun unwrap(): Vector2D = this
+
+    override fun Vector2D.wrap(): Vector2D = this
+}
+
+val Vector2D.r: Double get() = Euclidean2DSpace.run { sqrt(norm()) }
+
+@Suppress("FunctionName")
+fun Vector2D(x: Double, y: Double): Vector2D = Vector2DImpl(x, y)
+
+private data class Vector2DImpl(
+    override val x: Double,
+    override val y: Double
+) : Vector2D
+
+/**
+ * 2D Euclidean space
+ */
+object Euclidean2DSpace : GeometrySpace<Vector2D> {
+    fun Vector2D.norm(): Double = sqrt(x * x + y * y)
+
+    override fun Vector2D.distanceTo(other: Vector2D): Double = (this - other).norm()
+
+    override fun add(a: Vector2D, b: Vector2D): Vector2D =
+        Vector2D(a.x + b.x, a.y + b.y)
+
+    override fun multiply(a: Vector2D, k: Number): Vector2D =
+        Vector2D(a.x * k.toDouble(), a.y * k.toDouble())
+
+    override val zero: Vector2D = Vector2D(0.0, 0.0)
+
+    override fun Vector2D.dot(other: Vector2D): Double =
+        x * other.x + y * other.y
+}
\ No newline at end of file
diff --git a/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Euclidean3DSpace.kt b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Euclidean3DSpace.kt
new file mode 100644
index 000000000..dd1776342
--- /dev/null
+++ b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Euclidean3DSpace.kt
@@ -0,0 +1,57 @@
+package scientifik.kmath.geometry
+
+import scientifik.kmath.linear.Point
+import scientifik.kmath.operations.SpaceElement
+import kotlin.math.sqrt
+
+
+interface Vector3D : Point<Double>, Vector, SpaceElement<Vector3D, Vector3D, Euclidean3DSpace> {
+    val x: Double
+    val y: Double
+    val z: Double
+
+    override val size: Int get() = 3
+
+    override fun get(index: Int): Double = when (index) {
+        1 -> x
+        2 -> y
+        3 -> z
+        else -> error("Accessing outside of point bounds")
+    }
+
+    override fun iterator(): Iterator<Double> = listOf(x, y, z).iterator()
+
+    override val context: Euclidean3DSpace get() = Euclidean3DSpace
+
+    override fun unwrap(): Vector3D = this
+
+    override fun Vector3D.wrap(): Vector3D = this
+}
+
+@Suppress("FunctionName")
+fun Vector3D(x: Double, y: Double, z: Double): Vector3D = Vector3DImpl(x, y, z)
+
+val Vector3D.r: Double get() = Euclidean3DSpace.run { sqrt(norm()) }
+
+private data class Vector3DImpl(
+    override val x: Double,
+    override val y: Double,
+    override val z: Double
+) : Vector3D
+
+object Euclidean3DSpace : GeometrySpace<Vector3D> {
+    override val zero: Vector3D = Vector3D(0.0, 0.0, 0.0)
+
+    fun Vector3D.norm(): Double = sqrt(x * x + y * y + z * z)
+
+    override fun Vector3D.distanceTo(other: Vector3D): Double = (this - other).norm()
+
+    override fun add(a: Vector3D, b: Vector3D): Vector3D =
+        Vector3D(a.x + b.x, a.y + b.y, a.z + b.z)
+
+    override fun multiply(a: Vector3D, k: Number): Vector3D =
+        Vector3D(a.x * k.toDouble(), a.y * k.toDouble(), a.z * k.toDouble())
+
+    override fun Vector3D.dot(other: Vector3D): Double =
+        x * other.x + y * other.y + z * other.z
+}
\ No newline at end of file
diff --git a/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/GeometrySpace.kt b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/GeometrySpace.kt
new file mode 100644
index 000000000..b65a8dd3a
--- /dev/null
+++ b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/GeometrySpace.kt
@@ -0,0 +1,17 @@
+package scientifik.kmath.geometry
+
+import scientifik.kmath.operations.Space
+
+interface Vector
+
+interface GeometrySpace<V: Vector>: Space<V> {
+    /**
+     * L2 distance
+     */
+    fun V.distanceTo(other: V): Double
+
+    /**
+     * Scalar product
+     */
+    infix fun V.dot(other: V): Double
+}
\ No newline at end of file
diff --git a/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Line.kt b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Line.kt
new file mode 100644
index 000000000..d802a103f
--- /dev/null
+++ b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/Line.kt
@@ -0,0 +1,6 @@
+package scientifik.kmath.geometry
+
+data class Line<V: Vector>(val base: V, val direction: V)
+
+typealias Line2D = Line<Vector2D>
+typealias Line3D = Line<Vector3D>
diff --git a/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/ReferenceFrame.kt b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/ReferenceFrame.kt
new file mode 100644
index 000000000..420e38ce2
--- /dev/null
+++ b/kmath-geometry/src/commonMain/kotlin/scientifik/kmath/geometry/ReferenceFrame.kt
@@ -0,0 +1,4 @@
+package scientifik.kmath.geometry
+
+interface ReferenceFrame {
+}
\ No newline at end of file
diff --git a/settings.gradle.kts b/settings.gradle.kts
index 671db444a..a08d5f7ee 100644
--- a/settings.gradle.kts
+++ b/settings.gradle.kts
@@ -41,5 +41,6 @@ include(
     ":kmath-io",
     ":kmath-dimensions",
     ":kmath-for-real",
+    ":kmath-geometry",
     ":examples"
 )