Neural networks are increasingly used in computer technology. Due to their eciency in solving a wide range of problems, they are nding applications in all spheres of human activities. The aim of this work is to present an example of a neural network, to explain its structure in a simple way, and to demonstrate its potential in solving complex computational problems. Ap- plications of neural networks in science are discussed, with an emphasis on analysing astrophysical data, where usage of neural networks is very eci- ent. A historical overview, and an explanation of dierent types of machine learning, including neural networks, is discussed. Using simulated data from the MAGIC telescopes and an independently developed neural network code ZvijezdANNa in Python programming language, a classication of cosmic ray air showers into hadron origin and photon origin has been performed, resulting in 78% accuracy.