Congruences are a natural and convenient notation for formulating many interesting assertions in number theory. In this chapter, we introduce and work with congruences, we show how to solve linear congruences as well as discuss applications of congruences to parity check codes, e.g., the ones used in the ISBN-10 (International Standard Book Number) system. We will also use congruences to reformulate the problem in the quotation above and determine when such a problem has a solution. This result is commonly known as the Chinese remainder theorem.