The Encyclopaedia of Discrete Mathematics presents a through, Comprehensive Treatment of the subject using a Flexible Modular format. The Encyclopaedia is organized so that selected chapters in the book can either be studied together or used as a reference. The material in the Encyclopaedia is ideal for a freshman level in Computer Science or Mathematics. In addition, the author believes that the notion of proofs is important in most areas of study, and can be learned by any student, making it an effective alternative to the subject. The core of the Encyclopaedia consists of logical Reasoning ,Graph Theory, Binary Relations, Recurrence Relations, Combinatorics, Functions, Matrices. The remaining chapters can be selected according to individual course outlines.