Number theory is a branch of mathematics that primarily focuses on studying positive integers and their properties. Thus, it has often been considered the “purest” branch of mathematics because it was the furthest from any specific application. However, nowadays, number theory is considered one of the most important branches of mathematics for application in cryptography. This book is based on teaching materials from an undergraduate course Elementary Number Theory and graduate courses, Diophantine equations, and Diophantine Approximations and Application.

The book also provides an insight into subjects that are at the center of the research interest of the author of the book, as well as other members of the Croatian number theory research group. This book is primarily intended for undergraduate students who attend courses in number theory and its application. Also, it can be useful for advanced high school students who are preparing for competition in mathematics in which at all levels, from the school level competition to the international competition number theory, has a significant role. In addition, it is intended for graduate students and researchers in the fields of number theory, algebra, and cryptography.