I ask this question mainly because in the book "INTRODUCTION TO SMOOTH MANIFOLDS" by John Lee, it was stated that the reader is expected to have understanding in "fundamental group" and "covering space". When I google these terms, I find they are concepts in Modern Algebra which is a biggest gap in my Math knowledge.
Personally, I am not motivated to learn Pure mathematics in a most rigorous manner. I only want to learn the basics of some pure maths so that I can read the text that make use of them. So far, I have read 300 pages of point set topology,400 pages of real analysis, 300pages of functional analysis, but none for abstract algebra.
I know that Lee's "INTRODUCTION TO TOPOLOGICAL MANIFOLD" covered all I need for his book on Smooth Manifold. But, even that seems to expect basic knowledge in Group theory.
https://www.springer.com/us/book/9781441979391（Lee's "INTRODUCTION TO TOPOLOGICAL MANIFOLD“）
Can someone recommend me a readable book that allows me to quickly go through the basics of abstract algebra so that I can start with Lee's book on toplogical manifold? 500 pages of abstract algebra seem too intimidating.