There are numerous books which provide a general introduction to the problem and the history of its solution. The most popular one seems to be Simon Singh's Fermat's Enigma. Simon Singh also has a web site.
Additionally, PBS dedicated an entire episode of Nova to the investigation of the theorem and its solution by Andrew Wiles. The Nova episode is called The Proof. PBS has a web site.
The popular books and the Nova episode provide great background on the story and the significance of Wiles' proof. Unfortunately, they provide only a high level coverage of the proof's major ideas.
Many books have claimed to provide details for amateurs. I find all of these books to be very difficult. They are great for more advanced math students, but for most others, they can be quite a challenge.
- Fermat's Last Theorem for Amateurs - Explores the more elementary proofs.
- Notes on Fermat's Last Theorem - Great snippets. More a set of hints than actual proofs.
- Fermat's Last Theorem: A Genetic Introduction - Very in depth. Goes up to Kummer.
- Algebraic Number Theory and Fermat's Last Theorem - Very in depth. Broad coverage of Algebraic Number Theory.
In this blog, I will try to present details that bridge the gap between these works and Wiles' proof.