Topology optimization of structures and composite materials is a new and rapidly expanding field of mechanics which is now coming to play a major role in most branches of engineering, such as aerospace, mechanical, structural, civil and materials. There are also significant implications for energy production and the building and material sciences. It a truly 'high-tech' field, requiring advanced computer facilities and computational methods, while involving unusual theoretical considerations in pure mathematics. Topology optimization deals with some of the most intractable problems in the mechanical sciences, but is also of considerable practical interest in that it can achieve far greater savings than conventional (sizing or shape) optimization. Extensive research into topology optimization is being conducted in most developed countries.The present book describes the state of the art, bringing together researchers from a diversity of backgrounds: mathematicians, information scientists, aerospace, automotive, mechanical, structural and civil engineers.