In this talk, I’ll discuss the Arthur-Selberg trace formula, an essential tool in the study of automorphic representations. After stating the general form, I’ll go through some small examples where the trace formula is relatively simple, and then will describe how it complicates for groups like GL_n and SL_n. Time permitting, I’ll share an application of comparison of trace formulas in calculating multiplicities of automorphic representations (a result that features in the work of Jacquet-Langlands).