This is a very different introduction to proof techniques, which is usually found in an undergraduate textbook for a transition course in the US from a more computational approach to a proof-oriented approach. Although it starts from scratch, pointing out, always with well-chosen examples, the nature of proof by computation, by contradiction, by contrapositive, which makes that part similar to the above-mentioned textbooks, it quickly takes off to much more intricate landscapes, such as diagonalization and a plethora of inductive methods. The example used for proof by reduction is the fact that, given \(n\) points in the plane, finding their convex hull takes at least \(O(n\log n)\) steps. In the most important part of the book, the meticulous description, with examples, of an extraordinary wealth of types of induction proofs, we find, beyond simple and strong induction, Noetherian induction, induction on trees, together with a variety of transfinite inductive arguments, treated separately.