ar X iv : h ep - t h / 96 12 12 1 v 3 1 S ep 1 99 7 FOUR LECTURES ON M - THEORY

Synopsis: (i) how superstring theories are unified by M-theory; (ii) how superstring and supermembrane properties follow from the D=10 and D=11 supersymmetry algebras; (iii) how D=10 and D=11 supergravity theories determine the strong coupling limit of superstring theories; (iv) how properties of Type II p-branes follow from those of M-branes. Over the decade from 1984-94 superstring theory came to be regarded as the most promising approach to a unification of all the fundamental forces. The most compelling argument in its favour is that it naturally describes an ultraviolet finite and unitary perturbative quantum gravity 1. That this is true only in a spacetime of ten dimensions (D=10) is not so much a problem as an invitation to find a realistic model of particle physics by compactification to D=4 2. However, D=10 'superstring theory' is not a single theory but actually a collection of five of them. They are 3 4 is the one favoured in attempts to make contact with particle physics, the other four are equally acceptable as pertur-bative theories of quantum gravity (whereas the bosonic string is not because of the tachyon in its spectrum). In the infinite tension limit each of these five superstring theories is approximated by its effective field theory, which is an anomaly-free D=10 su-pergravity theory 5,6. There are also five of these but one of them, N=1 supergravity/Yang-Mills (YM) theory with gauge group U (1) 496 , is not the