In this chapter we introduce the notion of polynomial-time reductions. We explain how this technique can be used to transform an input for problem A to an input for problem B, mapping yes-instances for A to yes-instances for B and vice versa. If this transformation can be done in polynomial time, this implies that if B is polynomial-time computable, then so is A; also, it implies that if A has an exponential-time lower bound, then so must B. These polynomial-time reductions are thus a powerful technique to relate problems to each other. We will demonstrate several reduction strategies, namely reduction by restriction, by local replacement, and by component design. We include several exercises for practicing this technique.