In this chapter we begin by deriving the T duality perturbative symmetry of string theory from the world-sheet viewpoint in section 17.1. Although there is no complete formulation of string theory, the maximal supergravity theories in ten dimensions, studied in chapter 13, are the low energy effective actions for the type II strings. They are complete in that they contain all perturbative and all non-perturbative corrections. We will explain how these theories allow us to understand aspects of string theory that go beyond the well-understood perturbative regime. In particular, we will explain how the surprising exceptional group symmetries that the maximal supergravity theories possess are likely to be symmetries of string theory when suitably discretised. These symmetries have many features in common with the old electromagnetic duality symmetry of Maxwell's equations, whose generalisation are symmetries of the N = 4 supersymmetric Yang-Mills theory in four dimensions. This result is discussed in section 17.2.

We then discuss the connections between the maximal supergravity theories which suggest that there are corresponding connections between the string theories and an elevendimensional theory, usually called M theory. Finally we give an account of the conjectured E11 symmetry of an underlying theory of strings and branes.