Introduction to Number Theory in Mathematics Contests is a project divided into three volumes: Books 1, 2, and 3. This is Book 1 of the three-part series and contains an introductory part and basic concepts of the division theorem, divisibility, and congruences. Readers are introduced to a short exposition of the fundamentals on numbers. This book assumes that the audience is already familiar with some fundamental concepts such as sets, functions in general, and particular functions such as exponential and logarithmic, polynomials, or algebraic equations.

The authors' main goal is to establish a strong connection with the readers in the hopes of increasing their understanding of number theory and inspiring them to discover the beauty of number theory.

Several topics are discussed, such as the division theorem, divisibility, congruences, prime numbers and the unique factorization theorem (the fundamental theorem of arithmetic), which are the most important tools for understanding more advanced subjects in number theory. Different concepts are gradually explained, in their natural order, making the exposition self contained. Topics presented have several examples, theorems, and lots of problems to complete each chapter. Most of the problems have full solutions (in many cases more than one), but the authors strongly advise the reader to try solving each problem independently before reading the solution provided.