Many practical control problems are dominated by characteristics such as state, input and operational constraints, switches between different operating regimes, and the interaction of continuous-time and discrete event systems. At present no methodology is available to design controllers for such systems in a systematic manner. This book introduces a new design theory for controllers for such constrained and switching dynamical systems and leads to algorithms which systematically solve control synthesis problems. The first part of the book is a self-contained introduction to multiparametric programming, which is the main technique used to study and compute state feedback optimal control laws. The main objective is to derive properties of the state feedback solution, as well as to obtain algorithms to compute it efficiently. The focus is on constrained linear systems and constrained linear hybrid systems. The applicability of the theory is demonstrated through two experimental case studies: a mechanical laboratory process and a traction control system developed jointly with the Ford Motor Company in Michigan.