This text is a carefully structured, coherent, and comprehensive course of discrete mathematics. The approach is traditional, deductive, and straightforward, with no unnecessary abstraction. It is self-contained including all the fundamental ideas in the field. It can be approached byanyone with basic competence in arithmetic and experience of simple algebraic manipulations. Students of computer science whose curriculum may not allow the study of many ancillary mathematics courses will find it particularly useful. Mathematics students seeking a first approach to courses such asgraph theory, combinatorics, number theory, coding theory, combinatorial optimization, and abstract algebra will also enjoy a clear introduction to these more specialized fields. The main changes to this new edition are to present descriptions of numerous algorithms on a form close to that of areal programming language. The aim is to enable students to develop practical programs from the design of algorithms. Students of mathematics and computer science seeking an eloquent introduction to discrete mathematics will be pleased by this work.