If traders can't make money with trading, they start a consulting firm, offer trading courses, and write trading books. Consequently there are tons of books about trading methods and systems; most are useless, some are worse. Fortunately, a few trading books have been written by competent authors. Here's a non-complete list of useful books about theory and practice of automated trading:

Murray R. Spiegel, Larry J. Stephens: Schaum's Outline of Theory and Problems of Statistics. Beginner's course into probability and statistics with lots of examples. Work through this book and you have all basic knowledge for understanding financial math.

Ruey S. Tsay, Analysis of Financial Time Series. If you read the Schaum's Outline book and hadn't had enough of mathematics, this is the hard stuff that introduces all important mathematical models of price series.

Urban Jaekle, Emilio Tomasini: Trading Systems. How to develop a trading strategy; the book walks you through every step from idea up to various optimization and money management methods. Highly recommended.

David Aronson, Evidence-based Technical Analysis. Excellent, but a little elaborate book about the theory of testing trade strategies. A classic.

Ernest P. Chan, Quantitative Trading. Insight in strategy testing and portfolio optimization with many practical advices.

John F. Ehlers, Cybernetic Analysis for Stocks and Futures. Trading from an engineer's perspective with signal processing methods. Comes with source code for all trading algorithms.

Ralph Vince, Handbook of Portfolio Mathematics. How to allocate your capital in an optimal way among different assets and strategies.

William R. Gallacher, Winner Take All. Although we don't agree to all of Gallacher's conclusions about trade strategies, this book (from 1994) is a funny read and an intelligent insight into the trading scene and its gurus. The author also describes a apparently profitable trade system and then shows why it won't work - unique for a trading book.

Robert Harris, The Fear Index. A must-read for any automated trader...

If you come across other useful trading books, please list them here!