Introduction -- Functions optimization -- Elements of variational calculus -- Generalities concerning the optimal control problems -- The maximum principle (Pontryagin) -- The gradient method -- Dynamic programming (Bellman method) -- Heat transfer processes -- Heat exchangers -- Storage of thermal energy and exergy -- Heating and cooling processes -- Optimization of thermal insulation of seasonal water storage tanks -- Optimization of pin fin profiles -- Optimization of solar energy collection systems -- Flat-plate solar collectors. Optimization of absorber geometry -- Optimal time-dependent operation of open loop solar collector systems -- Optimal time-dependent operation of closed loop solar collector systems -- Optimal flow controllers -- Endoreversible heat engines -- Diesel engines -- Optimization of Daniel cam engines -- Photochemical Engines -- Optimization of one dimensional slider bearings. .