This monograph presents the results of scientific research in the field of mathematical modeling of complex non-stationary gas filtration processes in a porous medium. The issues of developing a mathematical and numerical model, as well as effective numerical algorithms for solving problems of monitoring, analysis and forecasting of the main indicators of gas field development are considered. In the applied aspect, the developed mathematical apparatus is of interest in solving the problems of analysis and design of the development of gas fields. The material presented in the book is intended for students, researchers, doctoral students, university professors and specialists of scientific and professional interests related to modeling complex processes of oil and gas filtration in a porous medium.