Adaptivity is an essential tool in modern scientific and engineering computation that allows one to optimize the computational effort by locating the degrees of freedom where they are most needed, that is in regions of rapid solution variation. Adaptive finite element methods (AFEM) are the most popular and effective numerical methods to solve elliptic PDE, and are driven by a posteriori error estimators. In this tutorial we will discuss the basic structure of AFEM and its main properties, analyze its convergence (contraction property), and derive convergence rates.