Lawrence Conlon, "Differentiable Manifolds", second edition, Birkhauser Advanced Texts.
Both of the above will be on reserve at the Taylor library.
Chris Isham, "Modern Differential Geometry for Physicists" (second edition), World Scientific. A very nice introduction to topology, differentiable manifolds, Lie groups and fibre bundles. It doesn't cover Riemannian geometry. (The first edition is in the library, and doesn't cover topology. The second edition is available from amazon.ca for C$36.)
William Boothby, "An Introduction to Differentiable Manifolds and Riemannian Geometry", Academic Press. Similar to Conlon's book. On reserve at the Taylor library.
Barrett O'Neill, "Semi-Riemannian Geoemtry, with applications to relativity", Academic Press. The first three chapters give a concise treatment of the material we will cover (except for differential forms).
R.W.R. Darling, "Differential Forms and Connections", Cambridge University Press. Covers almost exactly the topics we will cover, with a focus on differential forms.