This monograph, recommended as a scientific and methodological publication, is devoted to the presentation of the theoretical foundations (equations, laws, relations, etc.) of fluid and gas mechanics and methods of hydraulic calculation of pipelines and hydraulic networks of various geometric configurations under various external traffic conditions and consumer loads. Methods of kinematics, statics, and dynamics of homogeneous ideal and viscous media, as well as elements of the dynamics of rheological liquids and multicomponent gas mixtures, are described. The main theoretical positions and methods of solving applied problems in the field of hydrodynamics and aerodynamics of flows used as working substances moving through cross-sections of flow channels heterogeneous in geometric characteristics in the non-stationary mode of operation of industrial technological devices (hydraulic drives; components of thermal and mechanical equipment of thermal power plants; flow channels of turbine stages, etc.) are presented. This monograph is intended for students of technical specialties, as well as for undergraduates, doctoral students dealing with hydrodynamics and gas dynamics.