In recent years, the field of quantum computation has evolved to a promising research area, with the capacity to become as important as classical programming is today. This text serves as an introduction into the field of quantum computation. The main results are a proof that any quantum circuit can be implemented using a finite set of quantum gates, and a description of the principle and implementation of Shor’s algorithm. Furthermore, Shor’s algorithm is simulated on a classical computer to check if the procedure yields the results that are expected. This turns out to be the case.There are some aspects of this research that could be improved. The lower bound on the probability that Shor’s algorithm succeeds could be improved, and the classical simulation of Shor’s algorithm could be sped up as well by using a better implementation of the inverse Fourier transform.