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Some of the books, that I can remember, from my PhD reading list under Peter Petersen at Ucla 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.

A good place to get these was from "Book Scientific", where Spivak himself used to pick up the phone. They had an $800$ number.

Perhaps finally, I don't think it's necessarily that important whether there are alot of problems, because you should be primarily grappling with ideas and concepts, as opposed to just working problems. He did give me also a list of unsolved problems, which I have long since lost (maybe that's more what you were looking for!  ).

He also rated the journals, and recommended reading those. Annals of Mathematics and Journal of Differential Geometry, there were journals from Duke and Indiana university, there was the Pacific Journal of Mathematics, among others. Inventiones Mathematicae is also one of the best.

I think Lang's Algebra was probably on the list too. If not it probably should have been.

Some of the books that I can remember from my PhD reading list under Peter Petersen at UCLA 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.

A good place to get these was from "Book Scientific", where Spivak himself used to pick up the phone. They had an $800$ number.

Perhaps finally, I don't think it's necessarily that important whether there are a lot of problems, because you should be primarily grappling with ideas and concepts, as opposed to just working problems. He did also give me a list of unsolved problems, which I have long since lost (maybe that's more what you were looking for!)

He also rated the journals, and recommended reading those. Annals of Mathematics and Journal of Differential Geometry, there were journals from Duke and Indiana university, there was the Pacific Journal of Mathematics, among others. Inventiones Mathematicae is also one of the best.

I think Lang's Algebra was probably on the list too. If not, it probably should have been.

Some of the books, that I can remember, from my PhD reading list under Peter Petersen at Ucla 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.

A good place to get these was from "Book Scientific", where Spivak himself used to pick up the phone. They had an $800$ number.

Perhaps finally, I don't think it's necessarily that important whether there are alot of problems, because you should be primarily grappling with ideas and concepts, as opposed to just working problems. He did give me also a list of unsolved problems, which I have long since lost (maybe that's more what you were looking for! ).

He also rated the journals, and recommended reading those. Annals of Mathematics and Journal of Differential Geometry, there were journals from Duke and Indiana university, there was the Pacific Journal of Mathematics, among others. Inventiones Mathematicae is also one of the best.

Some of the books, that I can remember, from my PhD reading list under Peter Petersen at Ucla 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.

A good place to get these was from "Book Scientific", where Spivak himself used to pick up the phone. They had an $800$ number.

Perhaps finally, I don't think it's necessarily that important whether there are alot of problems, because you should be primarily grappling with ideas and concepts, as opposed to just working problems. He did give me also a list of unsolved problems, which I have long since lost (maybe that's more what you were looking for! ).

He also rated the journals, and recommended reading those. Annals of Mathematics and Journal of Differential Geometry, there were journals from Duke and Indiana university, there was the Pacific Journal of Mathematics, among others. Inventiones Mathematicae is also one of the best.

I think Lang's Algebra was probably on the list too. If not it probably should have been.

Some of the books, that I can remember, from my PhD reading list under Peter Petersen at Ucla 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.

A good place to get these was from "Book Scientific", where Spivak himself used to pick up the phone. They had an $800$ number.

Perhaps finally, I don't think it's necessarily that important whether there are alot of problems, because you should be primarily grappling with ideas and concepts, as opposed to just working problems. He did give me also a list of unsolved problems, which I have long since lost (maybe that's more what you were looking for! ).

He also rated the journals, and recommended reading those. Annals of Mathematics and Journal of Differential Geometry, there were journals from Duke and Indiana university, there was the Pacific Journal of Mathematics, among others.

Some of the books, that I can remember, from my PhD reading list under Peter Petersen at Ucla 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.

A good place to get these was from "Book Scientific", where Spivak himself used to pick up the phone. They had an $800$ number.

Perhaps finally, I don't think it's necessarily that important whether there are alot of problems, because you should be primarily grappling with ideas and concepts, as opposed to just working problems. He did give me also a list of unsolved problems, which I have long since lost (maybe that's more what you were looking for! ).

He also rated the journals, and recommended reading those. Annals of Mathematics and Journal of Differential Geometry, there were journals from Duke and Indiana university, there was the Pacific Journal of Mathematics, among others. Inventiones Mathematicae is also one of the best.