The adaptive finite element method (AFEM) is a powerful tool for numerical simulations. It is used to solve various problems of different kind numerically with high accuracy but less computational effort. This introductory talk explains key terms such as linear finite elements, a posteriori error estimators and adaptive mesh refinement. For a simple Poisson model problem the basic analytical setting such as the variational formulation is explained. The linear finite elements lead to a numerical discretization of the variational equation. In order to save computation time it is important to involve adaptivity into the algorithms. It will be explained what adaptivity means and how adaptive mesh refinement and a posteriori error estimates lead to the AFEM.