For another thread https://www.physicsforums.com/showthread.php?p=4420542 , I want to give simple motivations for the definition of two groups being isomorphic and related topics. My explanations have become so lengthy that I decided to post them here in 3 parts. ( They are probably too elementary for most readers of the other thread and that thread is already long.) I've read an explanation similar to mine somewhere. It made the reader work harder to find the isomorphisms. I picked notation that makes one of them blatantly obvious. The 3 messages will follow. Maybe they will be helpful to someone -and maybe they need some fixing.