Vacua of M-theory and N=2 strings

String and membrane dynamics may be unified into a theory of 2+2 dimensional self-dual world-volumes living in a 10+2 dimensional target space. Some of the vacua of this M-theory are described by the N=(2,1) heterotic string, whose target space theory describes the world-volume dynamics of 2+2 dimensional `M-branes'. All classes of string and membrane theories are realized as particular vacua of the N=(2,1) string: Type IIA/B strings and supermembranes arise in the standard moduli space of toroidal compactifications, while type {\\rm I}' and heterotic strings arise from a \\bf Z_2 orbifold of the N=2 algebra. Yet another vacuum describes M-theory on a {\\bf T}^5/{\\bf Z}_2 orientifold, the type I string on {\\bf T}^4, and the six-dimensional self-dual string. We find that open membranes carry `Chan-Paton fields' on their boundaries, providing a common origin for gauge symmetries in M-theory. The world-volume interactions of M-brane fluctuations agree with those of Born-Infeld effective dynamics of the Dirichlet two-brane in the presence of a non-vanishing electromagnetic field on the brane.