The starting point of this book is the concept of unique factorisation. Using an algebraic approach, the author introduces the reader to basic concepts on the border between algebra and number theory (integral domains, Euclidean rings, principal ideal domains, etc.) and, using them, he opens the door to number theory up to the level of quadratic fields, together with a moderate introduction to algebraic number theory. One of the appendices is devoted to quadratic reciprocity. The exposition contains a lot of details and exercises complement the exposition so that the book can also be used for self-study. The book can also be useful for instructors seeking an algebraically oriented complement for a standard text in elementary number theory.