Galerkin Finite Element Methods for Parabolic Problems The standard Galerkin method Semidiscrete methods based on more general approximations of the elliptic problem Smooth and non smooth data error estimates for the homogeneous equation Parabolic equations with more general elliptic operators Maximum Norm estimates Negative norm estimates and superconvergence Completely discrete schemes for the homogeneous equation Completely discrete schemes for the inhomogeneous equation Time discretization by the discontinuous Galerkin method A nonlinear problem The method of lumped masses The H1 and H1 methods A mixed method A singular problem.