Classical application areas of AI:
- Robotics
- Search
- Natural Language Processing
- Knowledge Representation / Expert Systems
- Planning / Scheduling
Various algorithmic approaches:
- Neural Networks
- Evolutionary / Genetic Algorithms
- Automatic Reasoning
- Logic Programming
- Probablilistic Approaches
Recommendable books:
- Norvig, Russel: Artificial Intelligence - A Modern Approach
- Norvig: Paradigms of Artificial Intelligence Programming (uses Lisp)
- Bratko: Prolog Programming for Artificial Intelligence
Recommendable programming languages:
- Prolog
- Lisp
- Java (many algorithms are discussed in Java nowadays)
There are also a number of interesting answers to this question (which sort of covers the same ground).
