Abstract: Calculating group cohomology for infinite groups is difficult in general. However, when a group acts on a tree, results from Bass-Serre theory allow for calculation. Two well-known examples of such groups are amalgamated products and HNN extensions. We use Bass-Serre theory and the Bockstein spectral sequence to determine the integral cohomology ring for the Bianchi groups, a family of arithmetic groups which admit descriptions as iterated amalgamated products and HNN extensions.