The Multi-Parametric Toolbox (MPT) is being developed at ETH Zurich to compute optimal or suboptimal feedback controllers for constrained linear and piecewise affine (PWA) systems. The toolbox provides a wide range of algorithms in a user-friendly format, covering various performance objectives and handling systems with disturbances and uncertainties. The algorithms are based on recent research in constrained optimal control. The MPT allows solving optimal control problems offline as functions of the initial state, resulting in a piecewise affine state feedback law. This method is efficient because online implementation only requires a set-membership test. The toolbox includes algorithms for constrained finite time optimal control (CFTOC) based on recent publications. Receding horizon control (RHC) is used to approximate constrained infinite time optimal control (CITOC), but it does not guarantee stability or constraint satisfaction. The MPT includes extensions to ensure these properties. It also provides minimax optimization for robust control under uncertainties. The toolbox also includes algorithms for PWA systems, which are powerful for approximating nonlinear systems and equivalent to hybrid systems. The MPT supports polytope manipulation, including convex hulls, unions, Minkowski sums, and more. It is based on state-of-the-art optimization packages and provides a transparent interface through object-oriented programming. The toolbox is free and compatible with various optimization tools. Polytopic sets are fundamental in multiparametric programming, and the MPT provides definitions and operations for polyhedrons.The Multi-Parametric Toolbox (MPT) is being developed at ETH Zurich to compute optimal or suboptimal feedback controllers for constrained linear and piecewise affine (PWA) systems. The toolbox provides a wide range of algorithms in a user-friendly format, covering various performance objectives and handling systems with disturbances and uncertainties. The algorithms are based on recent research in constrained optimal control. The MPT allows solving optimal control problems offline as functions of the initial state, resulting in a piecewise affine state feedback law. This method is efficient because online implementation only requires a set-membership test. The toolbox includes algorithms for constrained finite time optimal control (CFTOC) based on recent publications. Receding horizon control (RHC) is used to approximate constrained infinite time optimal control (CITOC), but it does not guarantee stability or constraint satisfaction. The MPT includes extensions to ensure these properties. It also provides minimax optimization for robust control under uncertainties. The toolbox also includes algorithms for PWA systems, which are powerful for approximating nonlinear systems and equivalent to hybrid systems. The MPT supports polytope manipulation, including convex hulls, unions, Minkowski sums, and more. It is based on state-of-the-art optimization packages and provides a transparent interface through object-oriented programming. The toolbox is free and compatible with various optimization tools. Polytopic sets are fundamental in multiparametric programming, and the MPT provides definitions and operations for polyhedrons.