This book addresses industrial model predictive controls (MPC), adaptive MPC, synthesis approaches of MPC and two-step MPC, with emphasis on synthesis approaches and the relationship between heuristic MPC and synthesis approaches. Chapter 1 introduces the concepts of system, modeling and MPC, including the description of transition from classical MPC to synthesis approaches. Chapters 2, 3 and 4 are concerned with model predictive heuristic control, dynamic matrix control and generalized predictive control, respectively. Chapter 5 talks about two-step MPC for systems with input nonlinearities. Chapter 6 concludes the main ideas in synthesis approaches of MPC. Chapters 7, 8 and 9 are concerned with synthesis approaches when the state is measurable. The polytopic description is mainly considered. This is one of the first works to systematically address robust MPC. Chapter 10 looks at synthesis approaches of output feedback MPC. This book presents an unbiased account of the significance of various MPC.