My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:

What is a good reference from which I could learn algebra necessary for studying algebraic topology.

I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$\pm\varepsilon$ pages.