This book written for everybody who would like to get introduced in that realm of human cognition that most differentiates us from all other creatures we know of in the universe. It is written to touch upon this faculty as the ultimate embodiment of thought in an age when the superficial and irrational is not only rife, but has become a dominating cultural expression of intellectual laziness. The danger of this culture forwarns the degeneration of civilisation into a society where unschooled minds appreciate the opinion of celebrity ignorants, military bullies, and the values of pop-up religions more than academia's systematically scrutinised wisdom. Such a culture stimulates the emergence of narrow mindedness, prejudice, and foolishness, feeding totalitarianism and oppression. We hereby join the battle that may ensure a tolerable existence for future generations, by expounding the virtues of critical thinking in its purest embodiment. We hope that this book will show how deeper meaning lurks beneath the skin of every man and woman. Anyone can harness the tools that can empower us to escape the relentless sea of puerile mass-culture. Allow us to persuade you with the allure of truth and the means to discover it. The book thoroughly covers propositional and predicate logic, set theory and functions, complexity theory and algorithm analysis as well as modal logic and model theory. It can be used for basic and also for more advanced studies in logic with a special focus on applications in systems science. The material there is suficient for 2-3 courses in logic and can be divided in two basic parts and a more advanced part. In this book, you will also find a large number of exercises together with solutions for a large number of selected problems.