The intention of this textbook is to provide both the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential algebraic equations An emphasis is placed on the interplay between the continuous optimal control problem which typically is defined and analyzed in a Banach space setting and discrete optimal control problems which are obtained by discretization and lead to finite dimensional optimization problems The book addresses primarily master and PhD students as well as researchers in applied mathematics but also engineers or scientists with a good background in mathematics and interest in optimal control The theoretical parts of the book require some knowledge of functional analysis the numerically oriented parts require knowledge from linear algebra and numerical analysis Examples are provided for illustration purposes Takes combined account of theory and numerics Includes optimality conditions and discretization methods Covers techniques for real time control feedback control and mixed integer optimal control Provides exercises and examples for use in courses