The first book you should read is your manual. I know, I know, that is not what you wanted to hear. But you really do need to read your manual to understand what your camera can do.
What’s after that? What is the first Digital Photogarphy Book you should get? I would suggest, funny enough, the Digital Photography Book, by Scott Kelby. After that, check out the book page here on my blog.
Why did I suggest that book? For one thing, you don’t need a DSLR to do lots of the stuff in this book. It is easy to read, and written with quite a bit of humor. What Scott says, is that he is trying to explain things to you as if you were a shooting buddy that went out shooting with him. Kelby himself says in the book, that this is not the most technical of books, and if you want more detail, you will need to find another book. What you will get are simple recipes and instructions on how to do certain types of photography, and how to get certain types of shots.
You will also get introduced to some new equipment. Do you have to buy it? No, but some things do require some extra gear to get the best results. Photography isn’t a cheap hobby, but make sure that what gear you buy will be worth it for you.
There are two other volumes in this series. They get more advanced and more in depth with each volume. You will get more into flash photography, and using some other gear. Start with the first volume. It will give you a good exposure to what you might want to do with photography, and what gear you might put on your wish list.