This book covers simple proof patterns such as case distinction, universal proof, and implication proof, as well as complex proof patterns like contraposition, proof by contradiction, diagonalization, and the various forms of complete induction up to transfinite induction. It provides answers to questions such as: What exactly is a proof by contradiction? Or a refutation? And how are they related? The authors attempt to discuss such questions by illustrating common proof patterns with generally understandable examples from everyday life, mathematics, and computer science.