When I was a baby undergrad, I was endlessly fascinated by the word group theory. It sounded so innocent, but whenever I opened a book about it, I was confronted with some very scary looking math. But group theory is not all that scary! So in this post, I’d like to explain what a group is (with some pictures). This is the explanation I wish I’d heard when I was first learning it. group theory is the study of symmetry Let’s look at this picture. It looks “symmetrical”. But what does that mean? Precisely, if you reflect it across the middle line, it looks the same. In other words, an object is “symmetrical”, if there is an action you can perform on it that leaves it looking the same. In this case, there are two actions you can perform: do nothing (that’s always one that we count) and flip across y-axis.