The work presented in this volume spans a period of some 40 years. In addition to more than 30 papers, a reprint of a 250-page book is also included—the much-admired A Collection of Mathematical Problems. The papers were selected on the basis of their individual significance, but taken together, they incidentally exhibit the broad range of fields to which Ulam has contributed. Among them are studies on the foundations of mathematics, set theory, measure theory, topology, probability theory, the Monte Carlo method (which was initiated by Ulam), the theory of computation, the use of computers for mathematical experimentation, and the applications of mathematics to astronomy, physics, and biology. Some of the papers cannot be categorized as belonging to any specific field: they are concerned with the cross-relationships between the methods of one field and those of another.