The book is devoted to the systematic presentation of theoretical foundations for setting problems of mathematical modeling of fluid and gas flows. Particular attention is paid to the construction of closed systems of equations for the turbulent regime of these currents. Turbulence models used in modern software complexes are considered in detail. The presentation of the material is made with the widespread use of the mathematical apparatus of direct (non-component) tensor calculus, brief information from which precedes this presentation. When recording physical relations in component form, a Cartesian rectangular coordinate system is used, since in modern software complexes only it is used for computational procedures.