This book presents a broad range of tools for designing mechanical systems, including kinematic and dynamic analysis of rigid and flexible multibody systems and their advanced optimization. The methodologies are presented from their fundamentals to the point where it is possible to build and analyze complex models of machines, vehicles or biomechanics. Design sensitivity and optimization methods are presented and applied to problems of design, reliability or parameter identification in cases of practical importance. The book is organized in a tutorial manner providing a comprehensive summary of current work in mechanical systems using advanced optimization methods, being suitable to students, researchers or industry engineers. Through applications to the design of machine components, transportation vehicles for ride, maneuverability and crashworthiness, or biomechanics, the reader can appraise the multidisciplinary aspects of the methodologies presented.