M theory, G₂-manifolds and four-dimensional physics

M theory on a manifold of G₂-holonomy is a natural framework for obtaining vacua with four large spacetime dimensions and = 1 supersymmetry. In order to obtain, within this framework, the standard features of particle physics, namely non-Abelian gauge groups and chiral fermions, we consider G₂-manifolds with certain kinds of singularities at which these features reside. The aim of this paper is to describe in detail how the above picture emerges. Along the way we will see how interesting aspects of strongly coupled gauge theories, such as confinement, receive relatively simple explanations within the context of M theory. We conclude with a brief discussion of the particle physics features of these vacua of M theory.