This is a very nice introduction to numerical analysis, in that it presents both theoretical results and practical algorithms in a similar easy to follow. It is very much a practical book in that ideas taken can be quickly implemented and tested on problems of the users interest. Readers unfamiliar with this book can see what others have said here.
To learn this material as well as possible I worked through a great number of the book's statements and expanded (with further detail) upon anything that was unclear to me at the time. You can find the material I had time to write up by following the links on this page.Book Notes: