Tumors are the result of accumulated genomic alterations that cooperate synergistically to produce uncontrollable cell growth. Although identifying recurrent alterations among large collections of tumors provides a way to pinpoint genes that endow a selective advantage in oncogenesis and progression, it fails to address the genetic interactions behind this selection process. A non-random pattern of co-mutated genes is evidence for selective forces acting on tumor cells that harbor combinations of these genetic alterations. Although existing methods have successfully identified mutually exclusive gene sets, no current method can systematically discover more general genetic relationships. We develop Genomic Alteration Modules using Total Correlation (GAMToC), an information theoretic framework that integrates copy number and mutation data to identify gene modules with any non-random pattern of joint alteration. Additionally, we present the Seed-GAMToC procedure, which uncovers the mutational context of any putative cancer gene. The software is publicly available. Applied to glioblastoma multiforme samples, GAMToC results show distinct subsets of co-occurring mutations, suggesting distinct mutational routes to cancer and providing new insight into mutations associated with proneural, proneural/G-CIMP, and classical types of the disease. The results recapitulate known relationships such as mutual exclusive mutations, place these alterations in the context of other mutations, and find more complex relationships such as conditional mutual exclusivity.