Number theory deals with the properties of natural numbers 1, 2, 3, ... Many of its problems, such as the twin prime problem or the famous Fermat's conjecture, can be stated in an easily understandable form, but their treatment usually requires sophisticated methods from algebra and analysis. These branches of mathematics owe their development in no small part to the fascination that number theory has exerted throughout history. The "queen of mathematics," as Gauss referred to number theory, was long considered the most beautiful yet also the most useless area of mathematics. Recently, this assessment has changed significantly due to the availability of fast computers. In particular, number-theoretic methods are now needed in coding theory and cryptography. The book sets out some.