The definition that I knew about groups were the abstract definition, that any set $G$ together with an operation $*$ is a group $(G,*)$ iff $G$ is closed under group operation, associative, and has inverse and identity element. But recently I watched Richard E Borchereds lectures on YouTube, which give a more concrete picture of groups by introducing groups as some symmetry elements acting on a set or some structures and introduced concepts like Cayley graphs. By these pictures we can associate a structure for any abstract group, that acts on it, which I came to know as Cayley theorem. These pictures are new to me.
Can anyone point me to some materials where I can read about these in details?