diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/NDStructure.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/NDStructure.kt
index 54e410ade..e458d0606 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/NDStructure.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/NDStructure.kt
@@ -174,6 +174,11 @@ public interface Strides {
      */
     public fun index(offset: Int): IntArray
 
+    /**
+     * Get next multidimensional index from the current multidimensional index
+     */
+    public fun nextIndex(index: IntArray): IntArray
+
     /**
      * The size of linear buffer to accommodate all elements of ND-structure corresponding to strides
      */
@@ -232,6 +237,10 @@ public class DefaultStrides private constructor(override val shape: IntArray) :
         return res
     }
 
+    override fun nextIndex(index: IntArray): IntArray {
+        TODO("Not yet implemented")
+    }
+
     override fun equals(other: Any?): Boolean {
         if (this === other) return true
         if (other !is DefaultStrides) return false
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
index 366acfb62..a5c00e8ec 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
@@ -164,11 +164,33 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
     }
 
     override fun RealTensor.transpose(i: Int, j: Int): RealTensor {
-        TODO("Alya")
+        val n = this.buffer.size
+        val resBuffer = DoubleArray(n)
+
+        val resShape = this.shape.copyOf()
+        resShape[i] = resShape[j].also { resShape[j] = resShape[i] }
+
+        val resTensor = RealTensor(resShape, resBuffer)
+
+        for (offset in 0 until n) {
+            val oldMultiIndex = this.strides.index(offset)
+            val newMultiIndex = oldMultiIndex.copyOf()
+            newMultiIndex[i] = newMultiIndex[j].also { newMultiIndex[j] = newMultiIndex[i] }
+
+            val linearIndex = resTensor.strides.offset(newMultiIndex)
+            resTensor.buffer.array[linearIndex] = this.buffer.array[offset]
+        }
+        return resTensor
     }
 
     override fun RealTensor.transposeAssign(i: Int, j: Int) {
-        TODO("Alya")
+        val transposedTensor = this.transpose(i, j)
+        for (i in transposedTensor.shape.indices) {
+            this.shape[i] = transposedTensor.shape[i]
+        }
+        for (i in transposedTensor.buffer.array.indices) {
+            this.buffer.array[i] = transposedTensor.buffer.array[i]
+        }
     }
 
     override fun RealTensor.view(shape: IntArray): RealTensor {
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt
index 0c10203f0..d6a6f5f16 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorStrides.kt
@@ -35,6 +35,23 @@ public inline fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): In
     return res
 }
 
+public inline fun nextIndex(index: IntArray, shape: IntArray, nDim: Int): IntArray {
+    val res = index.copyOf()
+    var current = nDim - 1
+    var carry = 0
+
+    do {
+        res[current]++
+        if (res[current] >= shape[current]) {
+            carry = 1
+            res[current] = 0
+        }
+        current--
+    } while(carry != 0 && current >= 0)
+
+    return res
+}
+
 
 
 public class TensorStrides(override val shape: IntArray): Strides
@@ -47,6 +64,9 @@ public class TensorStrides(override val shape: IntArray): Strides
     override fun index(offset: Int): IntArray =
         indexFromOffset(offset, strides, shape.size)
 
+    override fun nextIndex(index: IntArray): IntArray =
+        nextIndex(index, shape, shape.size)
+
     override val linearSize: Int
         get() = shape.reduce(Int::times)
 }
\ No newline at end of file
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt
index 86caa0338..8e95922b8 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/TestRealTensorAlgebra.kt
@@ -13,4 +13,55 @@ class TestRealTensorAlgebra {
         assertTrue(res.buffer.array contentEquals doubleArrayOf(11.0,12.0))
     }
 
+    @Test
+    fun transpose1x1() = RealTensorAlgebra {
+        val tensor = RealTensor(intArrayOf(1), doubleArrayOf(0.0))
+        val res = tensor.transpose(0, 0)
+
+        assertTrue(res.buffer.array contentEquals doubleArrayOf(0.0))
+        assertTrue(res.shape contentEquals intArrayOf(1))
+    }
+
+    @Test
+    fun transpose3x2() = RealTensorAlgebra {
+        val tensor = RealTensor(intArrayOf(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        val res = tensor.transpose(1, 0)
+
+        assertTrue(res.buffer.array contentEquals doubleArrayOf(1.0, 3.0, 5.0, 2.0, 4.0, 6.0))
+        assertTrue(res.shape contentEquals intArrayOf(2, 3))
+    }
+
+    @Test
+    fun transpose1x2x3() = RealTensorAlgebra {
+        val tensor = RealTensor(intArrayOf(1, 2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        val res01 = tensor.transpose(0, 1)
+        val res02 = tensor.transpose(0, 2)
+        val res12 = tensor.transpose(1, 2)
+
+        assertTrue(res01.shape contentEquals intArrayOf(2, 1, 3))
+        assertTrue(res02.shape contentEquals intArrayOf(3, 2, 1))
+        assertTrue(res12.shape contentEquals intArrayOf(1, 3, 2))
+
+        assertTrue(res01.buffer.array contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        assertTrue(res02.buffer.array contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0))
+        assertTrue(res12.buffer.array contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0))
+    }
+
+    @Test
+    fun transposeAssign1x2() = RealTensorAlgebra {
+        val tensor = RealTensor(intArrayOf(1,2), doubleArrayOf(1.0, 2.0))
+        tensor.transposeAssign(0, 1)
+
+        assertTrue(tensor.buffer.array contentEquals doubleArrayOf(1.0, 2.0))
+        assertTrue(tensor.shape contentEquals intArrayOf(2, 1))
+    }
+
+    @Test
+    fun transposeAssign2x3() = RealTensorAlgebra {
+        val tensor = RealTensor(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        tensor.transposeAssign(1, 0)
+
+        assertTrue(tensor.buffer.array contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0))
+        assertTrue(tensor.shape contentEquals intArrayOf(3, 2))
+    }
 }
\ No newline at end of file