General system theory (development, structure and system types, system and environment, system characteristics, principles of systematic approach). Tasks of analysis and synthesis of thermal process systems - TPS (elements and connection of TPS, interactions between TPS and environment, classification and properties of TPS, TPS hierarchy); Criteria of TPS efficiency, limitations in TPS design and operation; Methods of analysis and synthesis of TPS, (block schemes, mirroring the physical to the mathematical model, mathematical model recording method, objective function in mathematical models, connection equations, limitation system, determination of optimal parameters). TPS mathematical models (mathematical model classification, block and graphs models, schematic, parametric and matrix display), Mathematical models (record, steady and unsteady state of the system, the degrees number of freedom of the system, determination of the number of state parameters of TPS); Mathematical models assembly methods (static and dynamic models); Theoretical methods of mathematical models assembly (application of the law of conservation of mass, the law of conservation of energy, the law of conservation of momentum); Block-diagram method and informational variables method; Experimental methods for mathematical models assembly (active, passive, adaptation and combined); Adequacy of mathematical models (distributed and concentrated parameters); Examples of mathematical models and simulations in TPS (processes of the first and second order).