The topic of this course will be the global trace formula for a reductive group over a number field. We shall begin with a brief overview of the subject, taking motivation from the case of compact quotient. We shall then prove as much of the general formula as we can. In the process, we shall introduce the orbital integrals and characters, and their weighted variants, that are the main terms in the trace formula. The deeper study of these local objects will be the subject of the course of Kottwitz, and the lectures of DeBacker and Hales in the final week. General applications of the trace formula will actually require two successive refinements, the invariant trace formula and the stable trace formula. If time permits, we shall discuss these refinements, and the local problems of comparison whose solutions are required for applications.