Lisp dates back to John McCarthy in the late 1950s. At the time it had no peer as a language for symbolic computation. Current dialects Common Lisp and Scheme are used, e.g., for programming in artificial intelligence. The dialects are quite different from each other.
The Revised(5) Report on the Algorithmic Language Scheme is the definitive book on the language; it can be downloaded . Scheme is used in the introductory programming course at MIT. Their textbook Structure and Interpretation of Computer Programs by Abelson, Sussman and Sussman is a good introduction.
Lisp is based on very few, primitive concepts and has many, many predefined words.
This introduction centers on functional programming using a subset of words as suggested by Andrew Kitchen. An older version of this introduction was based on Common Lisp.