
Paul Wilmott on Quantitative Finance, Second Edition provides a thoroughly updated look at derivatives and financial engineering, published in three volumes with additional CD-ROM. Volume 1: Mathematical and Financial Foundations; Basic Theory of Derivatives; Risk and Return. The reader is introduced to the fundamental mathematical tools and financial concepts needed to understand quantitative finance, portfolio management and derivatives. Parallels are drawn between the respectable world of investing and the not-so-respectable world of gambling. Volume 2: Exotic Contracts and Path Dependency; Fixed Income Modeling and Derivatives; Credit Risk In this volume the reader sees further applications of stochastic mathematics to new financial problems and different markets. Volume 3: Advanced Topics; Numerical Methods and Programs. In this volume the reader enters territory rarely seen in textbooks, the cutting-edge research. Numerical methods are also introduced so that the models can now all be accurately and quickly solved. Throughout the volumes, the author has included numerous Bloomberg screen dumps to illustrate in real terms the points he raises, together with essential Visual Basic code, spreadsheet explanations of the models, the reproduction of term sheets and option classification tables.
If you really want to use it, I enjoyed the book Paul Wilmott on Quantitative Finance which uses the Bloomberg Terminal quite a bit for interactive learning.
Wikipedia the time value of money, valuation of perpetuities and annuities, modern portfolio theory, mean-variance optimisation, and related topics. Really understand these. Also check out the efficient market hypothesis and behavioural economics. Doing this via Wikipedia is probably better than some pre-packaged finance textbook because it's hard.
Start with bonds: Fabozzi's Handbook of Fixed Income Securities.
For equities first try Pricing the Future - it gives a rare historical context to the Black-Scholes equation. I suppose reading McKinsey's Valuation is good for understanding cash flow valuation. Hull's Options, Futures, and Other Derivatives is the cornerstone piece of the field, followed closely by Paul Wilmott on Quantitative Finance. If you get volatility you understand the liquid equity markets.
Now you understand basic theoretical finance and the entire capital structure (Google that).
Final building block is global macro (not college macroeconomics - you'll need to grab a textbook for that). For this I don't know of a good book. Fortunately, the IMF puts out solid Article IVs, analysts and economists write stuff everywhere, and the Fed, World Bank, WEF, IMF, and a host of other acronyms publish enough data that you can play with to get your feet wet.
From there it literally involves typing things into Amazon, and failing at that, Google, and failing at that, LinkedIn. More Money Than God gives a nice history of hedge funds. The Quants is a fun read of the newer players. You can Wikipedia banks' histories and financial crises.
Go through material because you're curious, not to get through it. Follow your curiosity down branches.
The Quora community has done a lot of good at fleshing out these questions.
Nassim Taleb's "Dynamic Hedging" is the finest book I'm aware of on the subject of actually trading/managing vol portfolios. It's REALLY good. And dense.
"Paul Wilmott on Quantitative Finance" vol 1-3 are worth having as a reference, perhaps.