This book discusses a number of selected results and methods, mostly from the areas of combinatorics and graph theory. The authors develop most topics to the extent that they can describe the discrete mathematics behind an important application of mathematics such as optimization problems, cryptography, and coding to name a few. Another feature that is not covered in other discrete mathematics books is the use of ESTIMATES (How many digits does 100! have? or Which is larger: 2^100 or 100!?). There are questions posed in the text and problems at the end of each chapter with solutions for many of them at the end of the book.