The Maple 15 DifferentialGeometry package is the most comprehensive mathematical software available in the area of differential geometry, with 224 commands covering a wide range of topics from basic jet calculus to the realm of the mathematics behind general relativity. It includes thorough documentation including extensive examples for all these commands, 19 differential geometry lessons covering both beginner and advanced topics, and 5 tutorials illustrating the use of package in applications. Key features include being able to perform computations in user-specified frames, inclusion of a variety of homotopy operators for the de Rham and variational bicomplexes, algorithms for the decomposition of Lie algebras, and functionality for the construction of a solvable Lie group from its Lie algebra. Also included are extensive tables of Lie algebras, Lie algebras of vectors and differential equations taken from the mathematics and mathematical physics literature.