We generated a global genetic interaction network for Saccharomyces cerevisiae, constructing 23.4 million double mutants, identifying ~620,000 negative and ~390,000 positive genetic interactions. Our network maps genetic interactions for essential gene pairs, highlighting essential genes as densely connected hubs. Genetic interaction profiles enabled assembly of a hierarchical model of cell function, including modules corresponding to protein complexes and pathways, biological processes, and cellular compartments. Negative interactions connected functionally related genes, mapped core bioprocesses, and identified multifunctional pleiotropic genes. Positive interactions often mapped general regulatory connections among gene pairs, rather than shared functionality. The global network illustrates how sets of genetic interactions occur within and between genes encoding complexes and pathways and how this topology can be exploited to explore genetic interactions underlying human disease.