This document is my attempt to explain the fundamental homomorphism theorem for groups, starting from basic definitions. The exposition is all in the introduction of the actual document, so you can read it there.
If you see any issues or want to point out potential improvements, feel free! Pull requests are welcome.
I'm idly considering turning this into a series. I could cover the other isomorphism theorems, for groups and potentially other algebraic structures as well. Kronecker's Theorem about the roots of polynomial equations would also be a fun project to tackle.