Of the many mathematical problems connected with general relativity, the extension problem has been chosen for discussion in this chapter, because it is concerned with the global geometrical and topological properties of Einstein manifolds, and those properties seem to me to constitute the most basically mathematical aspect of the theory. Although no use is made of formulas or results outside the preceding chapters of this book, the present chapter will probably be intelligible only to readers with some knowledge of relativity. In particular, the first two sections do not pretend to be in any sense a derivation of the principles of relativity, but merely a discussion of them.