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The ?rst and foremost goal of this lecture series was to show the beauty, depth and usefulness of the key ideas in computer science. While working on the lecture notes, we came to understand that one can recognize the true spirit of a scienti?c discipline only by viewing its contributions in the framework of science as a whole. We present computer science here as a fundamental science that, interacting with other scienti?c disciplines, changed and changes our view on the world, that contributes to our understanding of the fundamental concepts of science and that sheds new light on and brings new meaning to several of these concepts. We show that computer science is a discipline that discovers spectacular, unexpected facts, that ?nds ways out in seemingly unsolvable s- uations, and that can do true wonders. The message of this book is that computer science is a fascinating research area with a big impact on the real world, full of spectacular ideas and great ch- lenges. It is an integral part of science and engineering with an above-average dynamic over the last 30 years and a high degree of interdisciplinarity. The goal of this book is not typical for popular science writing, whichoftenrestrictsitselftooutliningtheimportanceofaresearch area. Whenever possible we strive to bring full understanding of the concepts and results presented.