In this chapter we describe the reduced basis (RB) method for parameterized partial differential equations (PDEs). We first describe the motivation for RB methods in the many-query and real-time contexts and the associated offline-online computational paradigm. We next introduce the framework for parameterized PDEs and the associated theoretical rationale for reduction. We then turn to projection techniques: formulation, a priori and a posteriori error estimation, and offline-online computational strategies. We next discuss techniques for identification of optimal approximation spaces, in particular the weak greedy approach. We emphasize linear elliptic PDEs, but we also consider nonlinear elliptic PDEs as well as linear parabolic PDEs.