The first book I'd recommend is Joy of Cooking. It's the reference encyclopedia--it tells you how to cook just about anything, plus it tells you the basic info on each type of ingredient--how to shop for it, how to clean or cut it, how to measure it, what the best techniques are for cooking it, etc. I suspect most cooks don't use it for the recipe collection, but instead as the volume to turn to when confronted with something new: "How do I deal with X?" It covers everything from how to boil eggs or make toast up to how to make Chateaubriand.
http://www.amazon.com/Joy-Cooking-Irma-S-Rombauer/dp/0743246268/ref=sr_1_1?ie=UTF8&qid=1420396210&sr=8-1&keywords=joy+of+cooking
Then, I think there are two books that will help with what you're asking--understanding how ingredients interact, so you can cook without a book. The first one is, "How to Cook Without a Book":
http://www.amazon.com/How-Cook-Without-Book-Techniques/dp/0767902793/ref=sr_1_1?ie=UTF8&qid=1420396132&sr=8-1&keywords=how+to+cook+without+a+book
The second one is "One Bite at a Time." It's written for cancer caregivers, and emphasizes recipes that are filled with healing minerals and are tolerated by those undergoing chemo. Never mind all of that. They're also easy, basic, and delicious recipes, many of them vegetarian (and many loved by picky DC's--black bean wraps with avocado "cream" were big in our house for a couple of years). The reason I recommend it is at the beginning of the book, she explains how to adjust a dish by tasting to balance the four flavor basics: Fat, Acid, Salt, or Sweet ("FASS"). It's easy to understand and she emphasizes you should always taste for FASS with every dish you cook. It's a great introductory lesson, and then, practice, practice, practice (taste, taste, taste).
http://www.amazon.com/One-Bite-Time-Revised-Nourishing/dp/1587613271/ref=sr_1_1?ie=UTF8&qid=1420396185&sr=8-1&keywords=one+bite+at+a+time