This book, "Introduction to Discrete Mathematics," is primarily aimed at students of Computer Science departments, as well as other departments where Computer Science is taught, and anyone interested in the subject of Discrete Mathematics. The book is the result of my teaching at the Department of Computer Science at the Technological Educational Institute of Thessaloniki, from its establishment (1987) until 2011. The goals of the book are aimed at: 1. Broadening the mathematical maturity of students during the study of a scientific area, which is quite different from the traditional coverage in basic Calculus. 2. Studying methods and techniques so that the student can solve problems that appear in various fields in computer science. 3. Developing students' abilities to create and solve such problems, interpret their solutions, and understand how to apply them. The book includes eight chapters, which contain the basic teaching topics of Discrete Mathematics covering the period of one semester. These are: - basic topics of Algebra of Logic, - introduction to Set Theory and Boolean Algebra with reference to logic circuits and switch circuits, - topics from Number Theory, - basic Counting rules with an introduction to Combinatorial Analysis, - Discrete Numerical Functions and Generating Functions - Recursive Relations, - broad introduction to Graph Theory, - elements from Trees with a description of the basic algorithms Dijkstra, Kruskal, etc. Each chapter contains several solved examples. Also, each chapter is accompanied by a sufficient number of unsolved exercises. In total, the solved examples and unsolved exercises are (approximately) 350 and 220 respectively. It is noted that each scientific term is accompanied by the corresponding English expression, so that the reader has easier access to the international bibliography.