Discrete mathematics is on the verge of becoming one of the most important areas of mathematical research, with applications in cryptography, linear programming, coding theory, and computer science. This book is aimed at students of mathematics and computer science who wish to develop an understanding of what mathematics is about, where it can be helpful, and what kinds of questions mathematicians deal with. The authors present a selection of results and methods from discrete mathematics, primarily from the fields of combinatorics and graph theory, but also partially from number theory, probability theory, and combinatorial geometry. Wherever possible, the authors have used proofs and problem-solving techniques to help students understand the solutions to the questions posed.