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## Main Question or Discussion Point

I'm currently taking graduate courses on differential geometry and algebra. What books are closest to the style of Rudin for these areas (i.e. rigorous, developing the theory in apropriate generality and being elegant at the same time).

For Algebra, I guess Lang is the bible, but what else is there? I would especially welcome some book that covers some advanced linear algebra, like symplectic and complex structures, matrix groups, etc.

For Differential Geometry, I have already tried a lot of books, but none of them really fit my needs. Kobayashi and Nomizu is almost unreadable for me and it deals mostly with bundles. On the other hand, there's Lee's Introduction to smooth manifolds, which has great list of topics, but I find his way of writing ugly. So topic-wise I'm searching for something like Lee, but done in a more elegant way. Is there anything like that?

For Algebra, I guess Lang is the bible, but what else is there? I would especially welcome some book that covers some advanced linear algebra, like symplectic and complex structures, matrix groups, etc.

For Differential Geometry, I have already tried a lot of books, but none of them really fit my needs. Kobayashi and Nomizu is almost unreadable for me and it deals mostly with bundles. On the other hand, there's Lee's Introduction to smooth manifolds, which has great list of topics, but I find his way of writing ugly. So topic-wise I'm searching for something like Lee, but done in a more elegant way. Is there anything like that?