Groups and Their Graphs by Israel Grossman and Wilhelm Magnus
Ever wondered about things symmetric? Surprisingly, there is an entire branch of mathematics that studies symmetry. Yes, you got me right. The symmetry you see in bee combs and kaleidoscope patterns, in the zigzag patterns of brick walls, the decorative patterns in Persian carpets or Celtic knots, the repetition in spiral stairs, the left/right mirror image of faces and animals, the swastika symbol or airplane and boat propellers or the fancy automobile stainless wheels, and also the three dimensional pattern on the soccer ball or the Geodesic dome .
One might wonder What is there to study about symmetry? It turns out lots. Mathematicians did not one day started to study symmetry. Rather, when trying to solve puzzling equations such as x^5 == y, mathematicians have gradually developed a body of theories, and over the centuries these got refined and abstracted, then they realized their theories is simply about symmetry. In the 1700s, their theories are aptly named Theory of Equations. In 1800s, it's abstracted form became Group Theory.
A very good intro to group theory for the non-professional is
i learned group theory from this book, in 1997. Get it.
Newer edition is:
It is this book that taught yours truly group theory. Your interest in group theory depends on how acquainted with math you are. Although group theory can be taught easily to children, but nevertheless it is very abstract. I recommend that you lean group theory only when you feel a need, which will come naturally when you read enough math. Otherwise, you may feel the subject quite pointless and dry.
For coders, if you don't know math, the most important and basic of math, is group theory. (other than basic calculus) learn it to start to get into serious math.
group theory, is something you can learn the basics in 1 hour. And you can spend 5 years getting phd specialization. It is also, one of the most simple and beautiful theory, and the most important, practical, widely used.
Another, even easier to read book than the above is