  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.
