diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BroadcastDoubleTensorAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BroadcastDoubleTensorAlgebra.kt
index 4bfbe5863..f315f6b51 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BroadcastDoubleTensorAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/core/BroadcastDoubleTensorAlgebra.kt
@@ -45,7 +45,7 @@ public class BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val newThis = broadcast[0]
         val newOther = broadcast[1]
         val resBuffer = DoubleArray(newThis.linearStructure.size) { i ->
-            newThis.buffer.array()[newOther.bufferStart + i] *
+            newThis.buffer.array()[newThis.bufferStart + i] *
                     newOther.buffer.array()[newOther.bufferStart + i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
@@ -85,7 +85,6 @@ public inline fun <R> BroadcastDoubleTensorAlgebra(block: BroadcastDoubleTensorA
 
 
 internal inline fun broadcastShapes(vararg shapes: IntArray): IntArray {
-    println(shapes)
     var totalDim = 0
     for (shape in shapes) {
         totalDim = max(totalDim, shape.size)
@@ -179,5 +178,59 @@ internal inline fun broadcastTensors(vararg tensors: DoubleTensor): List<DoubleT
         res.add(resTensor)
     }
 
+    return res
+}
+
+internal inline fun broadcastOuterTensors(vararg tensors: DoubleTensor): List<DoubleTensor> {
+    val onlyTwoDims = tensors.asSequence().onEach {
+        require(it.shape.size >= 2) {
+            throw RuntimeException("Tensors must have at least 2 dimensions")
+        }
+    }.any { it.shape.size != 2 }
+
+    if (!onlyTwoDims) {
+        return tensors.asList()
+    }
+
+    val totalShape = broadcastShapes(*(tensors.map { it.shape.sliceArray(0..it.shape.size - 3) }).toTypedArray())
+    val n = totalShape.reduce { acc, i -> acc * i }
+
+    val res = ArrayList<DoubleTensor>(0)
+    for (tensor in tensors) {
+        val matrixShape = tensor.shape.sliceArray(tensor.shape.size - 2 until tensor.shape.size).copyOf()
+        val matrixSize = matrixShape[0] * matrixShape[1]
+        val matrix = DoubleTensor(matrixShape, DoubleArray(matrixSize))
+
+        val outerTensor = DoubleTensor(totalShape, DoubleArray(n))
+        val resTensor = DoubleTensor(totalShape + matrixShape, DoubleArray(n * matrixSize))
+
+        for (linearIndex in 0 until n) {
+            val totalMultiIndex = outerTensor.linearStructure.index(linearIndex)
+            var curMultiIndex = tensor.shape.sliceArray(0..tensor.shape.size - 3).copyOf()
+            curMultiIndex = IntArray(totalMultiIndex.size - curMultiIndex.size) {1} + curMultiIndex
+
+            val newTensor = DoubleTensor(curMultiIndex + matrixShape, tensor.buffer.array())
+
+            for (i in curMultiIndex.indices) {
+                if (curMultiIndex[i] != 1) {
+                    curMultiIndex[i] = totalMultiIndex[i]
+                } else {
+                    curMultiIndex[i] = 0
+                }
+            }
+
+            for (i in 0 until matrixSize) {
+                val curLinearIndex = newTensor.linearStructure.offset(curMultiIndex +
+                        matrix.linearStructure.index(i))
+                val newLinearIndex = resTensor.linearStructure.offset(totalMultiIndex +
+                        matrix.linearStructure.index(i))
+
+                resTensor.buffer.array()[resTensor.bufferStart + newLinearIndex] =
+                    newTensor.buffer.array()[newTensor.bufferStart + curLinearIndex]
+            }
+        }
+        res += resTensor
+    }
+
     return res
 }
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
index c67687a09..feb8d11fa 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt
@@ -132,7 +132,7 @@ public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double, Dou
     override fun DoubleTensor.times(other: DoubleTensor): DoubleTensor {
         checkShapesCompatible(this, other)
         val resBuffer = DoubleArray(this.linearStructure.size) { i ->
-            this.buffer.array()[other.bufferStart + i] *
+            this.buffer.array()[this.bufferStart + i] *
                     other.buffer.array()[other.bufferStart + i]
         }
         return DoubleTensor(this.shape, resBuffer)
@@ -242,7 +242,63 @@ public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double, Dou
     }
 
     override fun DoubleTensor.dot(other: DoubleTensor): DoubleTensor {
-        TODO("Alya")
+        if (this.shape.size == 1 && other.shape.size == 1) {
+            return DoubleTensor(intArrayOf(1), doubleArrayOf(this.times(other).buffer.array().sum()))
+        }
+
+        var newThis = this.copy()
+        var newOther = other.copy()
+
+        var penultimateDim = false
+        var lastDim = false
+        if (this.shape.size == 1) {
+            penultimateDim = true
+            newThis = this.view(intArrayOf(1) + this.shape)
+        }
+        if (other.shape.size == 1) {
+            lastDim = true
+            newOther = other.view(other.shape + intArrayOf(1) )
+        }
+
+        val broadcastTensors = broadcastOuterTensors(newThis, newOther)
+        newThis = broadcastTensors[0]
+        newOther = broadcastTensors[1]
+
+        val l = newThis.shape[newThis.shape.size - 2]
+        val m1= newThis.shape[newThis.shape.size - 1]
+        val m2 = newOther.shape[newOther.shape.size - 2]
+        val n = newOther.shape[newOther.shape.size - 1]
+        if (m1 != m2) {
+            throw RuntimeException("Tensors dot operation dimension mismatch: ($l, $m1) x ($m2, $n)")
+        }
+        val m = m1
+
+        val resShape = newThis.shape.sliceArray(0..(newThis.shape.size - 2)) + intArrayOf(newOther.shape.last())
+        val resSize = resShape.reduce { acc, i -> acc * i }
+        val resTensor = DoubleTensor(resShape, DoubleArray(resSize))
+
+        for ((res, ab) in resTensor.matrixSequence().zip(newThis.matrixSequence().zip(newOther.matrixSequence()))) {
+            val (a, b) = ab
+
+            for (i in 0 until l) {
+                for (j in 0 until n) {
+                    var curr = 0.0
+                    for (k in 0 until m) {
+                        curr += a[i, k] * b[k, j]
+                    }
+                   res[i, j] = curr
+                }
+            }
+        }
+
+        if (penultimateDim) {
+            return resTensor.view(resTensor.shape.dropLast(2).toIntArray() +
+                    intArrayOf(resTensor.shape.last()))
+        }
+        if (lastDim) {
+            return resTensor.view(resTensor.shape.dropLast(1).toIntArray())
+        }
+        return resTensor
     }
 
     override fun diagonalEmbedding(diagonalEntries: DoubleTensor, offset: Int, dim1: Int, dim2: Int): DoubleTensor {
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt
index 73e3993a1..41c9b72f7 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt
@@ -47,6 +47,36 @@ class TestBroadcasting {
         assertTrue(res[2].buffer.array() contentEquals doubleArrayOf(500.0, 500.0, 500.0, 500.0, 500.0, 500.0))
     }
 
+    @Test
+    fun broadcastOuterTensors() = DoubleTensorAlgebra {
+        val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        val tensor2 = fromArray(intArrayOf(1, 3), doubleArrayOf(10.0, 20.0, 30.0))
+        val tensor3 = fromArray(intArrayOf(1, 1, 1), doubleArrayOf(500.0))
+
+        val res = broadcastOuterTensors(tensor1, tensor2, tensor3)
+
+        assertTrue(res[0].shape contentEquals intArrayOf(1, 2, 3))
+        assertTrue(res[1].shape contentEquals intArrayOf(1, 1, 3))
+        assertTrue(res[2].shape contentEquals intArrayOf(1, 1, 1))
+
+        assertTrue(res[0].buffer.array() contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        assertTrue(res[1].buffer.array() contentEquals doubleArrayOf(10.0, 20.0, 30.0))
+        assertTrue(res[2].buffer.array() contentEquals doubleArrayOf(500.0))
+    }
+
+    @Test
+    fun broadcastOuterTensorsShapes() = DoubleTensorAlgebra {
+        val tensor1 = fromArray(intArrayOf(2, 1, 3, 2, 3), DoubleArray(2 * 1 * 3 * 2 * 3) {0.0})
+        val tensor2 = fromArray(intArrayOf(4, 2, 5, 1, 3, 3), DoubleArray(4 * 2 * 5 * 1 * 3 * 3) {0.0})
+        val tensor3 = fromArray(intArrayOf(1, 1), doubleArrayOf(500.0))
+
+        val res = broadcastOuterTensors(tensor1, tensor2, tensor3)
+
+        assertTrue(res[0].shape contentEquals intArrayOf(4, 2, 5, 3, 2, 3))
+        assertTrue(res[1].shape contentEquals intArrayOf(4, 2, 5, 3, 3, 3))
+        assertTrue(res[2].shape contentEquals intArrayOf(4, 2, 5, 3, 1, 1))
+    }
+
     @Test
     fun minusTensor() = BroadcastDoubleTensorAlgebra {
         val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt
index 06aa3ebf7..168d80a9d 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt
@@ -79,6 +79,42 @@ class TestDoubleTensorAlgebra {
         assertTrue(expected.buffer.array() contentEquals assignResult.buffer.array())
     }
 
+    @Test
+    fun dot() = DoubleTensorAlgebra {
+        val tensor1 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        val tensor11 = fromArray(intArrayOf(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        val tensor2 = fromArray(intArrayOf(3), doubleArrayOf(10.0, 20.0, 30.0))
+        val tensor3 = fromArray(intArrayOf(1, 1, 3), doubleArrayOf(-1.0, -2.0, -3.0))
+
+        val res12 = tensor1.dot(tensor2)
+        assertTrue(res12.buffer.array() contentEquals doubleArrayOf(140.0, 320.0))
+        assertTrue(res12.shape contentEquals intArrayOf(2))
+
+        val res32 = tensor3.dot(tensor2)
+        assertTrue(res32.buffer.array() contentEquals doubleArrayOf(-140.0))
+        assertTrue(res32.shape contentEquals intArrayOf(1, 1))
+
+        val res22 = tensor2.dot(tensor2)
+        assertTrue(res22.buffer.array() contentEquals doubleArrayOf(1400.0))
+        assertTrue(res22.shape contentEquals intArrayOf(1))
+
+        val res11 = tensor1.dot(tensor11)
+        assertTrue(res11.buffer.array() contentEquals doubleArrayOf(22.0, 28.0, 49.0, 64.0))
+        assertTrue(res11.shape contentEquals intArrayOf(2, 2))
+
+        var tensor4 = fromArray(intArrayOf(10, 3, 4), DoubleArray(10 * 3 * 4) {0.0})
+        var tensor5 = fromArray(intArrayOf(10, 4, 5), DoubleArray(10 * 4 * 5) {0.0})
+        assertTrue(tensor4.dot(tensor5).shape contentEquals intArrayOf(10, 3, 5))
+
+        tensor4 = fromArray(intArrayOf(10, 3, 4), DoubleArray(10 * 3 * 4) {0.0})
+        tensor5 = fromArray(intArrayOf(4, 5), DoubleArray(4 * 5) {0.0})
+        assertTrue(tensor4.dot(tensor5).shape contentEquals intArrayOf(10, 3, 5))
+
+        tensor4 = fromArray(intArrayOf(4, 2, 1, 3, 8, 1), DoubleArray(4 * 2 * 1 * 3 * 8 * 1) {0.0})
+        tensor5 = fromArray(intArrayOf(5, 1, 2, 8, 3, 1, 5), DoubleArray(5 * 1 * 2 * 8 * 3 * 1 * 5) {0.0})
+        assertTrue(tensor4.dot(tensor5).shape contentEquals intArrayOf(5, 4, 2, 8, 3, 8, 5))
+    }
+
     @Test
     fun testContentEqual() = DoubleTensorAlgebra {
         //TODO()