Steutel (probability, emeritus, Eindhoven University of technology, The Netherlands) and Van Haarn (mathematics, Free University, The Netherlands) present new developments together with a full account of the theory of infinite divisibility, dealing only with probability distributions on the real line and with divisibility with respect to convolution and the addition of independent random variables. They provide methods for making decisions on the infinite divisibility of a given distribution, with emphasis on criteria in terms of distribution functions and probability densities. Chapters cover infinitely divisible distributions on nonnegative integers and real lines, self- decomposability and stability, mixtures, and infinite divisibility in stochastic processes.