What is the relevance of Discrete Mathematics? On the one hand, it is the Mathematics that arises in daily life (including logic, the art of sound reasoning). On the other hand, as computers have only finite states, Informatics is in a sense applied Discrete Mathematics. In fact, we will see that cryptography, the science of secure transmission of information between computers, strongly relies on mathematical concepts. As such, one could even argue that the importance of Mathematics is not only scientific, but political. In this volume, the authors present a self-contained introduction to discrete mathematics the science of finite and countably infinite structures. In addition to taking a theoretical approach, they also include many practical exercises. The text covers a broad range of topics such as propositional logic, set theory as well as detailed treatments of combinatorics and graph theory. This is complemented by an extensive introduction to modern cryptography, including the RSA cryptosystem, "postquantum" systems, and the numbertheoretic and algebraic prerequisites thereof.