These are the notes from my Discrete Mathematics lectures, delivered primarily to students in Communication and Electrical Engineering at Sapienza University of Rome. The course is roughly divided into the following parts: Elements of Number Theory Elements of Modern Algebra Elements of Combinatorics Elements of Graph Theory The objective of these lectures was to illustrate various topics across the broad areas of modern mathematics into which Discrete Mathematics is traditionally divided. Additionally, I aimed to take an “experimental” approach to the material, frequently encouraging students, whenever feasible, to use computers and computer algebra systems to conduct their own experiments. Given the wide range of potential topics, it was challenging to select a single textbook that encompassed everything I wanted to cover - and only that. Consequently, I consulted numerous sources, all of which are acknowledged in the bibliography and recommended for further study. The book contains also numerous solved exercises.