I want to learn some homological algebra from Weibel's book. After reading section 1.1 and 1.2, I find I lack knowledge of abelian category. In section 1.2, Weibel says the constructions on modules in section 1.1 can be applied to arbitrary Abelian category. However, I can't see how to form a quotient (like quotient module) and what the homology is in an abelian category.
I currently have some knowledge in Category theory (Using Emily Riehl's "Category theory in context"), such as limit, adjoint, and monad. But I don't have knowledge of Abelian category. Both Weibel's appendix and CWM treat Abelian category too sketchy, especially on the definition of homology.
I'd prefer that you recommend books or notes that have a complete introduction to Abelian category.
Edit: Thank you very much for the books recommended! I think I have found a note that can meet my needs: The first several sections of homological algebra (chapter 12) in The Stacks project seems to be a concise and enough introduction to abelian categories used in homological algebra.