* Code examples
* History (when/who first used it)
* Application examples
The classic textbooks are:
* "Algorithms" by Robert Sedgewick et al.
* "Introduction to Algorithms" by Cormen et al.
part 1 or is this:
Fascicles is a new effort by Knuth and is more hardware oriented.
It's under the "Develop a strong understanding of algorithms and data structures" part.
The former has the best exercises (borderline mathematical), but is lightest on implementation. The latter has the best introductory pedagogy and has implementation code, but is not what I would use if I want to grok algorithms deeply.
People keep recommending Cormen. He's the book you get AFTER you understand algorithms. Cormen reads more like a reference manual. Cormen can substitute in for Skiena in a pinch. Skiena sounds like the one you want most of all though.
Algorithm Design [Kleinberg, Tardos] (2005)
It also contains instructive exercises and answers.