I recommend The Complete Book of Tai Chi Chuan by Wong Kiew Kit. Take my advice with a grain of salt; although I studied tai chi for a couple years, I never made progress beyond the beginner stage.
From the back cover:
- The history and development of various styles
- The basic set of movements
- The physical and mental benefits of Tai Chi Chuan
- The relationship of Tai Chi to Taoism
The history of tai chi is debated. The Chinese martial arts tend to embellish their origin stories with elements of ancestors and the fantastic.
The usual caveats for martial arts book resources apply:
It is not easy for beginners to learn any martial art from a book; it is even harder to learn internal arts like Tai Chi Chuan
The description of movements covers common fundamental movements and forms from multiple styles of tai chi, including a Chen style form. I don't know whether this will match what you are learning.
The study of tai chi is not for the short term:
In my opinion, the practising Tomoi or Siamese Boxing is probably the fastest way one can learn to fight
In my personal opinion, the portions of the preface are most useful to understand the book's contents:
Nevertheless, practising patiently does not mean following a method blindly. If a student who has patiently practised Tai Chi Chuan for many years still remains sickly, weak, or emotionally unstable or mentally dull, then he or she has not been judicious or wise. Such a person should either turn to something else, or seek more information from masters or books to improve his or her practice. Generally, people who have correctly practised an established method for a year should reap the benefits that method is reputed to bring.
Although Tai Chi Chuan has a rich philosophy, usually recorded in poetic language, and some examples are found in this book, it is geared towards practical use in combat, and more significantly, in our daily life. In other words, if you have practised Tai Chi Chuan for 20 years, but cannot yet defend yourself when an assailant attacks you, or are still prone to anger or nervousness, or lack the energy to run and jump irrespective of how old you are, you have wasted your time. This book explains why and how Tai Chi Chuan enhances your health, work, and play.