The aim of this textbook is not only to provide an elegant route through the theoretical fundamentals of computer science, but also to show that theoretical computer science is a fascinating discipline, full of spectacular contributions and miracles, and depth in research, and yet directly applicable. Thus, we aim to excite people about its study. To achieve these goals we do not hesitate to take a lot of space to present motivations, and especially to give the informal development of crucial ideas and concepts and their transparent, but rigorous presentation.