Our purpose in writing this book was to provide a clear, accessible treatment of discrete mathematics for students studying graduate or post graduate courses in Mathematics, Computer Science and Engineering. The goal of the book is to lay the mathematical foundation for computer science courses such as data structures, algorithms, relational database theory, automata theory and formal languages, compiler design, and cryptography, and for mathematics courses such as linear and abstract algebra, combinatorics, logic and set theory, and number theory. It is written as a text book for the course at Graduation level or Post-Graduation level for all fields of sciences and engineering. There are several materials in this text book, so anyone can select the topics according to his/her need for their respective university/college examinations. This is also enriched with many interesting and harder sums in solved examples as well as in exercises.