One I would recommend is:
http://www.amazon.com/Corporate-Finance-3rd-Pearson/dp/01329...
This will go into some level of detail into all areas.
Once you are comfortable with this material, you can branch into more deeper study in each area.
A lot of trading systems attempt to exploit arbitrage opportunities (however time limited) in the market place. A book like the above will give you a deeper understanding of the stock market and the different financial instruments that are used in the market.
It will also provide real insight into how companies manage their capital budgeting (I have $100 million dollars, how do I decide what to spend this money on this year). Not every company will follow the same approach, but the fundamental concept of net present value is very common.
Once you have a good understanding of the basics then you can delve further into derivatives. It would be hard to get into derivatives without a solid background in what a MBA/graduate level corporate finance book gives you.
As an aside, anyone in IT that wants to expand their business know-how would gain quite a bit by reading a corporate finance book. If you want to know what the executive team spends their time on, the knowledge around capital budgeting and understanding how projects are assessed (ie. using WACC and NPV) is very valuable.
E.g. there's no need to know all about leasing or taxes or mergers in order to price derivatives. In fact I doubt that most people working in the area know much about corporate finance, whether they are math and physics PhDs working as quant researchers or regular programmers implementing the models.
But if one has no clue about how stock markets work, how risk is quantified, the intricacies of call and put options, the various types of bonds, etc. than I would suggest a corporate finance book is a good place to start.
Why? It starts slow and builds the concepts on top of each other. These books take a long time to put together and they are usually pedagogically well put together. Just for this along I would recommend such a book. The effort that has been put together to make sure that students have the best opportunity to easily pick up the knowledge is really high.
I especially like the above book as it builds the concept of the law of one price and arbitrage very well.
I have made the assumption that kevincrane is at this starting point.
The reality of all this is that this stuff is hard.
It's quite amazing much the study of finance is so complex. A corporate finance book let's you gaze into the window without actually stepping inside.
As I suggested, its a starting point.
In my opinion, if one can't get their head around the knowledge in a corporate finance book the rest of the material in the more technical focused books on that book list will not be very accessible. There is a reason why people in the field have Masters and PhD's in strong heavy math focused specializations.
"Principals of Corporate Finance" (Brealey & Myers) is the definitive newbie handbook for Corporate Finance, which is not the same subject as Quant Finance.
If you'd like more of a live view into what is going on in the markets (strategy-wise), check out nuclearphynance.com.
As for technical books, I prefer Maureen O'Hara's structural approach over continuous time finance. Beyond providing more of a "trader's view", she is also a lovely person. I don't much care for continuous time finance.