Riccardo Rebonato - Modern Pricing of Interest-Rate Derivatives: The LIBOR Market Model and Beyond

In this book Ricardo Rebonato, well-known academic and practitioner, reviews all important models for pricing Interest-Rates derivatives. The book is somewhere in between the book by Bjork and the book by Musiela and Rutkowski in terms of mathematical difficulty. Ricardo begins with the lucid introduction to bond analysis and stochastic processes, so you can begin you journey with this book and you don't need any prior knowledge.
This book is especially highly rated at all exotics trading desks.

Mark S. Joshi - C++ Design Patterns and Derivatives Pricing

The book by Mark S. Joshi, who is the one of the real world practicioners (as far as I remember he works for RBS) , tries to teach you how to code clearly and efficiently. I think that you should be thinking of reading this book after you learn basics from the Daniel Duffy's book.

Daniel J. Duffy - Financial Instrument Pricing Using C++

If you want to become a quant trader (statistical arbitrage for example), you will need a stron programming skills. The book by Daniel J. Duffy (almost Darrel Duffie ;) ) will help you to equire necessary skills. The book is considered to be one of the most sucessful books on C++ in finance.

Marek Musiela, Marek Rutkowski - Martingale Methods in Financial Modelling

If you want to write a PhD in asset pricing you will need this book. It is very practical and result oriented. Two Marek's (one of them was teaching me one day :D ) did an excelent job and provided a lucid and readable book. Almost all significant areas of asset pricing are covered in this textbook. I really recommend it to all, who want to become a Quants. If you are planning to become a trader a book by Tomas Bjork would be more than enough. :)

Darrel Duffie - Dynamic Asset Pricing Theory

This is my favorite book to asset prices. If you ask any professor on any ivy league university in the United States or in UK about the best book about asset pricing, you will get this book in answer for sure. The book is very condense review of a number of most significant results in asset pricing. It starts with discreet time settings and then moves to continous time analysis.

The book is less useful in practical setting than the book by Musiela and Rutkowski, but it is much better in developing the intuition behind the results. This is a top choice for any PhD researcher.

Karatzas Shreve - Brownian Motion and Stochastic Calculus

I found the book by Ioannis Karatzas and Steve Schreve to be the most intuitive introduction to stochastic processes. Most important topics are covered extremely well in this book. Number of motivating examples comes from quantitative finance.

Bernt Oksendal - Stochastic Differential Equations: An Introduction with Applications

Solid knowledge of stochastic calculus is necessary to fully benefit from reading advanced asset pricing text books (Duffie or Musiela and Rutkowski). Oksendal is one of the books that provide pretty intuitive tretment of the topic. The book covers number of topics including a solution to Hamiltonian Jakobi Bellman problem (HJB equation).

Tomas Bjork - Arbitrage Theory in Continuous Time

This is rigorous, but introductory, treatment of continous time finance. "Arbitrage Theory in Continous Time" by Tomas Bjork is a great book that should serve a prime textbook in all MFE courses. The book starts with the lucid introduction to asset pricing in discreet time. Than the author develops the intuition behind the stochastic calculus. The pace of the book is just right. After the necessery notation of stochastic calculus is developed the author reviews the most important models of continous time asset pricing up to the LIBOR market model.

James Douglas Hamilton - Time Series Analysis

The time series analysis is a must for every statistical arbitrage quant trader.The book by James Douglas Hamilton is a perfect and up-to-date review of all basic time-series techniques. You can find here topics such as:

• Vector Error Correction Model - Full Information Maximum Likelihood estimation of cointegrating vectors.
• Stochastic Volatility Models - GARCH, FIGARCH etc.
• Generalized Method of Moments
• Kalman Filter

This is a book with high level of PhD mathematics. A little bit simpler book that covers same topics is "New Introduction to Multiple Time Series Analysis" by Helmut Lütkepohl.

Obstfeld Rogoff - Foundations of International Macroeconomics

Understanding Macroeconomics maybe quite important at some point of your carrer as a quant trader.
The book by Maurice Obstfeld and Kenneth Rogoff is a very lucid introduction to the open-macro economics. You will gain the intuition of interest rates movements and exchange rate dynamics. I would say that this MSc/PhD level book is actually everything you to build proper understanding of International Macroeconomics. The books by Carl Walsh - "Monetary Theory and Policy, 2nd Edition" or the book by Michael Woodford "Interest and Prices: Foundations of a Theory of Monetary Policy" are to advanced and impractical. These books are rather for PhD researchers.

Nassim Nicholas Taleb - Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets

The book by Nassim was phenomenal success. It is by far the most successful popular book about trading that was published at the beginning of this century. Taleb is writing about the fact that most people do not have probabilistic intuition. This observation exposes a number of puzzling in real-life.

It would be best if you read the book of Taleb, after you read "Market Wizards" of Schwager. First book will temper you optimism (trading is easy...!) after you read the "Wizards".

Definitely the must-read for anyone who wants to become a trader.

Jack D. Schwager - The New Market Wizards: Conversations with America's Top Traders

That is the second part of the famous book. I am sure that if you found the first interesting you will love this one too. As always Jack Schwager is able to make a great use of these interviews and the depth of the analysis of the strategy of each of these traders makes the book an invaluable source of information for every beginner.

Jack D. Schwager - Market Wizards

I believe that this is the first and most important book that every wanna be trader should read. Jack did really a great job, when he made interviews with some of the greatest minds of trading. If you read this book you will learn that there are many different trading strategies that may be profitable. Each of these strategies require different personality, and you can find a trading system that will be best for you. The book does not require any maths. In fact there is no single equation in the whole book and you would be able to read it in one or two night. I really recommend!