Foreword. Introduction.- Part I Modelling water infiltration in soils. 1 Brief overview of unsaturated flow concepts. 2 Settlement of the mathematical models of nonhysteric infiltration.- Part II Analysis of infiltration models. 3 Basic existence theorems for evolution equations. 4 Functional approach to the quasi-unsaturated infiltration. 5 Functional approach to the saturated-unsaturated infiltration model.- Part III Inverse problems in infiltration. 7 Identification of the boundary conditions from recorded observations.- Part IV Appendix.