The principle of induction and the related principle of strong induction have been introduced in the previous chapter. However, it takes a bit of practice to understand how to formulate such proofs. In this chapter, we will illustrate both methods with several examples. Furthermore, we discuss a far-reaching generalization of these methods called well-founded induction and illustrate this method of proof by investigating properties of the Ackermann function. The chapter concludes with a discussion of recursion, recursively defined sets, and structural induction.