This book is an introduction to the numbers theory, also known as ""higher arithmetic. It starts with a discussion of the notion of divisibility and deals with the elementary properties of congruences; it studies the existence of roots and quadratic congruences, concluding with the study of some grade 2 and 3 diophantine equations in addition to the known Pell equation. The author focuses on the topic of cryptography, one of its applications ranging from the first chapters and covers topics as recent as Rabin cryptosystems, without the method ceasing to be elemental.