This comprehensive theory of water flow and solute transport in porous media summarizes recent developments of the last decade of stochastic modelling of subsurface flow and transport at different scales. One of the main topics is the analysis of the effects heterogenous natural formations exert upon water flow and contaminant transport. This text is suited for graduate courses, ideally supplemented by exercises at the end of most chapters. Researchers and engineers will find the conceptual foundations and the mathematical tools needed in order to model water flow and contaminant transport in aquifers.