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.