Ultraviolet Behavior of N = 8 supergravity

In these lectures the author describes the remarkable ultraviolet behavior of N = 8 supergravity, which through four loops is no worse than that of N = 4 super-Yang-Mills theory (a finite theory). I also explain the computational tools that allow multi-loop amplitudes to be evaluated in this theory - the KLT relations and the unitarity method - and sketch how ultraviolet divergences are extracted from the amplitudes