Covering algebra prerequisites for an intro to Algebraic Topology from Munkres

I am a senior year physics student currently enrolled in a Topology course offered by the math department. The first half of the course is basic point set topology (first 4 chapters of Munkres) and the second half is an intro to algebraic topology (first chapter of Hatcher and ch 9 - 11 of Munkres). Apparently, the instructor forgot to mention in the course outline that some knowledge of abstract algebra will be assumed for the second part of the course. Munkres' book himself states in his preface that "we do assume familiarity with the elements of group theory" for the second portion of the book. I have some elementary knowledge of what a group is from my physics courses but that's pretty much all I know about abstract algebra. I need to quickly get a grasp of all the notions I need before the course progresses to the 2nd part. Could anyone suggest be a good book to cover the necessary prerequisites? I am looking for somethinking that is concise and gets the job done as quickly as possible. For context, my math background includes 2 courses in real analysis (at the level of Tao's books), LA at the level of Axler's book, Munkres' Analysis on Manifolds and Functional Analysis at the level of Kreyzig's book.