Some of the books, that I can remember, from my PhD reading list under Peter Petersen at Ucla for doctorate in Riemannian Geometry which I never completed were: _Characteristic Classes_,by Stasheff, _Morse Theory_, Milnor, _Dimension Theory_, Hurewicz and Wallman, _The Topology of Fibre Bundles_, Steenrod. We both agreed that Spivak's $5$ volume _Comprehensive Introduction to Differential Geometry_ was quite useful. There was Galot, Hulin and La Fontaine's _Riemannian Geometry_. I'll update this if I remember anything else. It seems to me that Milnor's _Topology from the Differentiable Viewpoint_ might have been also, and Spivak's _Calculus on Manifolds_ probably wasn't, but I enjoyed it. I also had a copy of his _Riemannian Geometry_ in manuscript form, which is now available in the GTM series.