Reddit mentions of Your Body, Your Yoga: Learn Alignment Cues That Are Skillful, Safe, and Best Suited To You

I know you said one, but I'm going to recommend two books as a totally comprehensive study. The first is Light on Yoga because it's a complete compendium of all the asanas you'll ever want to do with step by step instructions. However there a no modifications in the book itself.

For that, I highly recommend Your Body Your Yoga by Bernie Clark. (https://www.amazon.com/Your-Body-Yoga-Alignment-Skillful/dp/0968766536/ref=sr_1_1?ie=UTF8&qid=1486140527&sr=8-1&keywords=your+body+your+yoga)
It's an extremely thorough explanation of body mechanics and is enlightening for figuring out how and why your body moves and how to listen to make sure your modifying asanas so they work best for you.

Between the two, you'll have an understanding of asana and how to make them work for you. If you're savvy, you should be able to get both books slightly used, or even new for about $20 (check abebooks.com and amazon 3rd party sellers).

Lastly, if you're truly on a budget and can't afford to get both at once, or want to preview the books before you buy, check out your library. Even if they don't own the books, you should be able to request them through interlibrary loan. This is what I did, I think I borrowed over 20 books over the course of 3 months and eventually settled on the two I mentioned above as a "complete" home yoga library that I use regularly.