For linear algebra, Sheldon Axler's _Linear Algebra Done Right_.
For analysis, Stephen Abbott's _Understanding Analysis_.
These two books will give you a very solid grounding in the undergraduate linear algebra and analysis. Personally, I also worship the style of Baby Rudin (it's the nickname of his _The Principles of Mathematical Analysis_), but it can be too dry to many people.
These two books will give you a very solid grounding in the undergraduate linear algebra and analysis. Personally, I also worship the style of Baby Rudin (it's the nickname of his _The Principles of Mathematical Analysis_), but it can be too dry to many people.