Although sometimes not the most rigorous, this book provides a firm foundation of Analysis and is definitely the best book I have found for learning concepts.
Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book What is Mathematics?, co-written with Herbert Robbins.
This is an excellent introduction to multivariate calculus and contains more interesting applications than any other textbook I have seen. As good as the book is, I gave it 4 stars. It is marred by errors in the excersices and the main text. Additionally, it has far fewer interesting exercises than the first volume, which I rated 5 stars.