The Shape of Space

General Relativity tells us that all massive objects deform the backgrounds into which they are placed so that the very shape of space is changed by their presence. If, in addition, these objects happen to be charged, they give rise to a flux which distorts the background still further. In the talk, we will apply these simple ideas to gather information about the elusive 11-dimensional M-theory which gives rise to string theory. We will try to categorize some of the geometries that are allowed in M-Theory by studying what happens to a background when stable hyper-dimensional objects called BPS M-branes are brought into it.