In the following chapter we address the techniques for the resolution of some celebrated recurrence relations. We will discuss in detail the linear recurrences with constant coefficients. Our emphasis goes to the application of the theory: the proofs, though elementary, are relegated to the end of the chapter. We proceed step by step in showing first how to solve just homogeneous recurrences, then how to find a particular solution in some special cases and only finally how to obtain all the solutions to the original problem. We also consider linear recurrences with variable coefficients and the divide and conquer recurrences: here we focus on the order of magnitude of the solutions, a fact which has an impact in the analysis of algorithms. There are about 40 examples and 50 classified problems.