Testing General Relativity with Gravitational Waves

In the next few years, physicists will make the first direct detection of the phenomenon called gravitational waves. These waves, which are propagating perturbations in the metric that describes the geometry of space-time, are Einstein's last unconfirmed prediction. Among the most interesting science we will be able to accomplish with these observations is in the area of testing General Relativity. In this dissertation, I give a brief introduction to General Relativity and gravitational waves, and then spend the bulk of the document explaining how we can test General Relativity using gravitational waves. In particular, I focus on the data analysis techniques that will be necessary for performing such tests.