These two volumes constitute the Proceedings of the `Conférence Moshé Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity. With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena. Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.