The past fifty years have witnessed a dramatic growth of mathematical research, the evolution of ideas and new branches. It has become virtually impossible for any mathematician to keep track of all these developments even at a superficial level. This unique book not only attempts a history of contemporary mathematics, but also provides some authoritative guidance through the maze of mathematical theories. Neither encyclopaedic nor superficial, it addresses a rich range of topics from the personal viewpoint of more than forty mathematicians, most of them active researchers and renowned specialists in their fields. The volume is complemented by relevant statistical and bibliographic material and illustrated with some 200 portraits of mathematicians. Together with Development of Mathematics 19001950 (edited by J.-P. Pier, Birkhduser 1994) it constitutes a comprehensive reference work of lasting value on the unfolding of mathematical concepts in the twentieth century.