diff --git a/neuronal_network.c b/neuronal_network.c
index 2a88e73..c2661dd 100644
--- a/neuronal_network.c
+++ b/neuronal_network.c
@@ -188,6 +188,88 @@ void train_network(Neural_Network* network, Image *image, int label) {
     Matrix* hidden3_outputs = apply(sigmoid, add(dot(network->weights_3, hidden2_outputs), network->bias_3));
     Matrix* final_outputs = apply(sigmoid, add(dot(network->weights_output, hidden3_outputs), network->bias_output));
 
+
+    //begin backpropagation:
+    Matrix* sigma = matrix_create(final_outputs->rows, 1);
+    matrix_fill(sigma, 1);
+    Matrix* temp_1 = subtract(sigma, final_outputs);
+    Matrix* temp_2 = multiply(temp_1, final_outputs); // * soll-ist
+    Matrix* temp_3 = matrix_create(final_outputs->rows, final_outputs->columns);
+    matrix_fill(temp_3,0);
+    temp_3->numbers[label][0] = 1;
+    Matrix* temp_4 = subtract(temp_3, final_outputs);
+    sigma = multiply(temp_2, temp_4);
+
+
+    matrix_free(temp_3);
+    matrix_free(temp_4);
+    //sigma done
+
+    Matrix* temp1 = transpose(hidden3_outputs);
+    Matrix* temp2 = dot(sigma, temp1);
+    Matrix* weights_delta = scale(temp2, network->learning_rate);
+    Matrix* bias_delta = scale(sigma, network->learning_rate);
+
+
+
+    Matrix* temp = add(weights_delta, network->weights_output);
+    matrix_free(network->weights_output);
+    network->weights_output = temp;
+    temp = add(bias_delta, network->bias_output);
+    matrix_free(network->bias_output);
+    network->bias_output = temp;
+
+    matrix_free(weights_delta);
+    matrix_free(bias_delta);
+
+    // other levels
+
+    Matrix* sigma_current = matrix_create(hidden3_outputs->rows, 1);
+    matrix_fill(sigma_current, 1);
+    temp_1 = subtract(sigma_current, hidden3_outputs);
+    temp_2 = multiply(temp_1, hidden3_outputs); // *sum(delta*weights)
+
+    for(int j=0;j<hidden3_outputs->rows;j++) {
+        double sum = 0;
+        for (int i = 0; i < sigma->rows; i++) {
+            sum += hidden3_outputs->numbers[j][i]*sigma->numbers[i][0];
+        }
+        temp_1->numbers[j][0]=sum;
+    }
+    sigma_current = multiply(temp_2, temp_1);
+    // sigma done
+
+
+
+
+    temp1 = transpose(hidden2_outputs);
+    temp2 = dot(sigma_current, temp1);
+    weights_delta = scale(temp2, network->learning_rate);
+    bias_delta = scale(sigma_current, network->learning_rate);
+
+
+
+    temp = add(weights_delta, network->weights_3);
+    matrix_free(network->weights_3);
+    network->weights_3 = temp;
+    temp = add(bias_delta, network->bias_3);
+    matrix_free(network->bias_3);
+    network->bias_3 = temp;
+
+    matrix_free(weights_delta);
+    matrix_free(bias_delta);
+
+
+
+
+
+
+    matrix_free(temp_1);
+    matrix_free(temp_2);
+    matrix_free(temp1);
+    matrix_free(temp2);
+
+    //matrix_print(sigma);
 }
 
 //void batch_train_network(Neural_Network* network, Image** images, int size);