This book offers a nice introduction to fundamentals of number theory with an emphasis on Diophantine analysis and Diophantine approximation and their mutual interactions. In fifteen chapters and one appendix the reader will find many interesting basic principles and results, which can be used as a springboard to a deeper study of the subject. Besides standard material covered in similar books (such as classical approximation theorems, continued fractions, the Pell equation), the reader will also find chapters on the Roth theorem, the abc-conjecture, factorization with continued fractions, p-adic numbers, Hensel lemma and the local-global principle. Every chapter ends with exercises (more than 200 in total) of varying levels of complexity (the difficult ones are denoted by asterisks). Moreover, the text contains many historical notes, which can be helpful, especially for neophytes in the historical orientation of the subject. The book is written in a lively and lucid style and is principally self-contained and requires only standard mathematical background. It is thus aimed at not only graduate and advanced undergraduate students but to anyone interested in these important aspects of number theory.

Reviewer:

špor