TITLE: Rigorous Text in Multivariable Calculus and Linear Algebra
QUESTION [18 upvotes]: So I'm wanting a solid math book for Christmas.  I have a solid background in Calculus and am currently working through baby Rudin.  I really want a rigorous book dealing with multivariable calculus and linear algebra.  How well does Apostol II do this?  Would this be a good continuation book from my current study?  If not, what book would you suggest?
EDIT:  I really like Apostol's Multivariable Calculus and Linear Algebra book and its format.  Will this book accomplish my purpose?  Do you think it is a good book?

REPLY [13 votes]: The best book on this for beginners is John and Barbara Hubbard's Vector Calculus,Linear Algebra And Differential Forms: A Unified Approach, 3rd edition. It is an incredibly rich treasure trove of results, all presented with full rigor and with a striking amount of originality. What I love best about this book is that it balances rigorous mathematics with applications better then any textbook I've ever seen. It is a bit pricey, but now as a gift for Christmas, it's perfect since it'll be a lifetime investment for a serious student of mathematics. 
It's simply awesome, you're wasting your time buying anything else. (I'm not saying there's not any other good books on rigorous multivariable calculus-there certainly are. I just think any other book for a beginner is waste of money to buy. )