Artificial Intelligence (AI) is an academic discipline primarily concerned with creating the concept of the same name. The definitions of this concept can be split into four different classes;

Systems that think like humans.
Systems that act like humans.
Systems that think rationally.
Systems that act rationally.

Here are some textbook definitions of Artificial Intelligence, sorted into the four different classes;

Systems That Think Like Humans
"The exciting new effort to make computers think ... machines with minds, in the full and literal sense" (Haugeland, 1985)
"The automation of activities that we associate with human thinking, activities such as decision-making, problem solving, learning ... "
(Bellman, 1978)

Systems That Act Like Humans
"The art of creating machines that perform functions that require intelligence when performed by other people" (Kurzweil, 1990)
"The study of how to make computers do things at which, at the moment, people are better" (Rich and Knight, 1991)

Systems That Think Rationally
"The study of mental faculties through the use of computational models"
(Charniak and McDermott,1985)
"The study of the computations that make it possible to perceive, reason, and act"
(Winston 1992)

Systems That Act Rationally
"A field of study that seeks to explain and emulate intelligent behaviour in terms of computational processes" (Schalkoff, 1990)
"The branch of computer science that is concerned with the automation of intelligent behaviour"
(Luger and Stubblefield, 1993)

The reason behind this multitude of definitions is the amount of different research going on in AI. It is a subject that has links with many disciplines, including; Psychology, Philosophy, Linguistics, Physics, Computer Science, Cognitive Science, Neuroscience and Artificial Life.

Key figures in the modern development of AI are;
Alan Turing (the Turing Test, "Computing Machinery and Intelligence")
John McCarthy (LISP and Common Sense Reasoning)
McCulloch & Pitts (Neural Networks)
Norbert Wiener (Cybernetics)
John von Neumann (Game Theory)
Claude Shannon (Information Theory)
Newell & Simon (The Logic Theorist)
Marvin Minsky (Frames)
Donald Michie (Freddy)

According to Marvin Minsky in 1997, there are three basic approaches to AI: Case-based, Rule-based and Connectionist reasoning.   The idea in Case Based Reasoning (CBR) is that the program has many stored problems and solutions.  When a problem comes up, the computer tries to find similar problems in its database by finding aspects the problems share.  However it is very difficult to identify which aspects of a problem might match new problems. Rule-Based reasoning, or expert systems, consist of a large number of rules detailing what to do when encountering a different input.  Unfortunately you can't anticipate every single type of input, and it is very hard to make sure you have rules that will cover everything.   Connectionists use big networks of simple components similar to the nerves in a brain. Connectionists take pride in not understanding how a network solves a problem.  Unfortunatly this makes it very hard to make a soloution that works for more then one problem.

The top grad schools for the subject in 2002 are as follows;
Georgia Tech

"AI - A Modern Approach", Stuart Russel, Peter Norvig, 1995.
"Hal's Legacy", David Stork, 1997