In this chapter, we collect all required results from finite element analysis for elliptic PDEs. We restrict ourselves to consideration of linear finite elements on families of shape-regular and quasi-uniform meshes. We present a priori error estimates with respect to various norms for the solution of (linear) Poisson equation either with Dirichlet or Neumann boundary conditions, for problems with the right-hand side from a measure space, and for semilinear equations.