This book deals with the theory and practice of numerical simulation with respect to oil and gas production. It will compare classical reservoir engineering methods with numerical simulation. The basic equations of the fluid flow in the porous rocks are presented. Various functions necessary for the construction of the model are discussed, including PVT, relative permeability, capillary curve, etc. Explanations are given for the approximation of the differential equations of the flow in porous media using the difference equation technique (e.g. IMPES, fully implicit, semi-implicit etc.) and also for the linearization and the solution of the linear equation system of fluid flow (i.e. direct and iterative methods). The simulation methods of special cases of petroleum recovery processes - including fractured porous, fractured cavity reservoir, EOR and EGR methods - are summarized. Numerical modeling from the point of view of a reservoir engineer is analyzed and three practical examples are illustrated: two black oil models - one interference case and one underground gas storage - and a compositional simulation for EOR screening. The book is recommended for students, for engineers and for geoscientists who are engaged with crude oil-, natural gas- and water production located in underground structures and even for that specialist who deals with underground gas storages.