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The book is intended as a manual for a half-year introductory course of number theory. The aim is to present the theory to the extent which is indispensable to every mathematics student, regardless of their future specialization. The target points include the local methods, the Quadratic Reciprocity Law, the Prime Number Theorem, unique factorization of ideals in rings of algebraic integers in finite extensions of~Q, units in the rings of integers in quadratic extensions of~Q, and decomposition of primes in rings of integers. The authors' main aim was to show that the beauty of number theory lies in the fact that on the one hand it enriches other domains of mathematics, and on the other hand it makes frequent use of their methods and results. Each chapter is complemented with problems, of different complexity. Some solutions and hints are given at the end of the book.