If you’re taking quantum mechanics, QCD, quantum field theory, electricity and magnetism, or any of the other physics courses where group theory is often used, but rarely explained, then Groups and Their Graphs by Israel Grossman and Wilhelm Magnus is the book for you. It lays out the basics of group theory in simple easy to understand language. For the more esoteric minded, it even covers quaternions.
I just found this book a few weeks ago and finally picked up my own copy. It’s from a seemingly brilliant series of books called the New Mathematical Library that was started in the ‘60s. The series takes advanced or less than common mathematical concepts and explains them in a manner that is targeted at an audience with high school level math skills. Here’s a quote from the book:
"This book is one of a series written by professional mathematicians in order to make some important mathematical ideas interesting and understandable to a large audience of high school students and laymen. Most of the volumes in the New Mathematical Library cover topics not usually included in the high school curriculum; they vary in difficulty, and, even within a single book, some parts reuire a greater degree of concentration than others. Thus, while the reader needs little technical knowledge to understand most of these books, he will have to make an intellectual effort."
The book uses geometric operations such as rotations and flips on an equilateral triangle to illustrate concepts so far. While it’s easy to understand, it never talks down, or dumbs down concepts. More on this later.