String theory is a theoretical framework in physics which replaces point particles with vibrating strings. This seemingly small modification to normal physics has profound implications - consistency conditions place tight restrictions on the possible theories one can write down. For example, string theory is mathematically consistent only if the number of dimensions of spacetime is 10. In the 1990's, five consistent string theories were known in 10 dimensions. After the discovery of various string dualities, it was conjectured that these five apparently different string theories were all different limiting cases of one theory - an 11 dimensional theory called M-theory. In this talk I will try to give an overview of T-duality, a string duality relating some of the five consistent string theories to one another. T-duality has a very geometric flavour, and has no analogue in point-particle physics - it is a purely stringy phenomenon.
Since this will be an overview talk, I won't assume any prior knowledge of string theory.