Solving Partial Differential Equations with Python and Finite Differences. In this talk we present a framework for solving Partial Differential Equations (PDEs) with the Finite Differences Method (FDM). We implement a flexible framework in Python for rapid prototyping of solvers for PDEs both for scalar and parallel computers. The framework provide an abstraction for FDM stencils realized as a class, and the problem is specified in terms of a set of stencils defined over some FDM grid. The framework provides both explicit and implicit solvers. In case of a parallel computer, the communication-patterns described by the stencils are used to optimize the distribution of unknowns on the available processors. This talk focus on the parallel aspects of the framework, as well as how fairly advanced solvers like e.g. multigrid solvers can be implemented using the set of stencils defining a problem as a linear operator.