Welcome to the Fashion Spot!!
Be aware that this book is really, really old ... I think it came out in the 80's. So, unless they have updated it, the colors may not be current. But I would say that the threory still is pretty good ... at least a good starting point to learn about color on various people. But you also need to learn about texture, body shape, balance, trends, and how to run and promote a small business.
I really haven't come across any really good books about how to be a personal stylist ... or how to set up and run your business, but I'm sure there are a wide assorment of books that can help.
There is one book, but it's more for stylists (wardrobe, hair, make up, manicurists) who work with photographers and models in the fashion/commercial world ... not for personal stylists. But it's got lots of very important information if you want to get into regular fashion styling:
http://www.crystalwrightlive.com/books-a-dvds.html
Of course, the more you learn about fashion in general, the better. So ... you should also refer to the following thread, which has a lot of recommendations about various designers and concepts and see if any might shed some light on fashion history and what's current.
Books About Fashion & Designers - Recommendations ?