Numerical Models for Differential Problems In this text we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic parabolic and hyperbolic linear equations but also the diffusion transport and Navier Stokes equations as well as equations representing conservation laws saddle point problems and optimal control problems. Furthermore we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements finite differences finite volumes spectral methods and domain decomposition methods and reduced basis methods. In particular we discuss the algorithmic and computer implementation aspects and provide a number of easy to use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines and recommendable to those researchers in the academic and extra academic domain who want to approach this interesting branch of applied mathematics