This work addresses the topic of differentiable programming as a new shift in perspective on the field of neural networks. The definition of adversarial attacks are presented, as well as their classification into two major groups: targeted and untargeted attacks. In the scope of this work, three different models were implemented and used for testing the theoretical background: two dense fully connected neural networks (with one and two hidden layers, respectively), and one convolutional model. The process of training these models is given, as well as a detailed description of the FGSM and PGD types of attacks. Further, the work presents a brief introduction to the TensorFlow library and the MNIST dataset. During the normal training procedure, the tested models achieved accuracies of 87%, 88% and 97% (respectively), while under adversarial attacks with perturbation of 0.1 the same models achieve accuracies of 0.6%, 0.8% and 2.3% (respectively) for the PGD type, and 3.6%, 1.3% and 27.9% for the FGSM type (respectively). By training the robust model, the accuracy was significantly improved, up to 87% for the perturbation value of 0.3. Additionally, this work also presents the software implementation of the described adversarial attacks.