We arc to admit no more causes of natural things (as we arc told by Newton) than such as are both true and sufficient to explain then- appearances. This central theme is basic to the pursuit of science, and goes back to the principle known as Occam's razor: ''if presented with a choice between indifferent alternatives, then one ought to select the simplest one.'' Unconsciously or explicitly, informal applications of this principle in science1 and mathematics abound.The conglomerate of different research threads drawing on an objective and absolute form of this approach appears to be part of a single emerging discipline, which will become a major applied science like information theory or probability theory. We aim at providing a unified and comprehensive introduction to the central ideas and applications of this discipline.Intuitively, the amount of information in a finite string is the size (number of binary digits, or bits) of the shortest program that without additional data, computes the string and terminates. A similar definition can be given for infinite strings, but in tiiis case the program produces element after element forever...