Here´s my two cents to it, organized in thematic blocks (as trading doesn´t consist of just one area)
- Psychology:
Read something about Behavioral Finance. BF is the smallest common denominator in the field of trading.
All books from Ari Kiev - IMO one of the best authors dealing with psychological issues.
-Technical Analysis:
John Murphy´s "Technical Analysis of the Financial Markets" is a pretty good introduction. If you already built a technical fundament, read "The Master Swing Trader". This book is a revelation
-Strategy:
As the most important aspect in trading is NOT psychology but its derivative, strategy, read some stuff on strategy,
such as the classic itself, Sun Tze´s "The Art of War".
If you´re less martialic, skip it and go over to game theory; this is the topic that will revolutionize the area of trading within the next years.
My recommendations: "Thinking strategically" and "Games and Decisions". Furthermore, try to find something about evolutionary game theory. This is what the financial markets are all about (my recommendation: "The Selfish Gene" by Richard Dawkins, "The Evolution of Cooperation" by Robert Axelrod).
-Classics:
Jesse Livermore wrote that "the business of speculation is so old, that nothing new can be discovered". Absolutely right, but the already discovered can be further enhanced.
So fetch some of the classics, basically the entire "Wileys Financial Classics" edition and the books from Humphrey B. Neill and Richard Wyckoff.
Remember, just my two cents.