Functional Analysis Notes is somewhat similar to Topology. Actually, topology can be seen as the deeper researching about various space. Functional analysis mainly focuses on these types of space: Metric space, Banach space, and Hilbert space. The theories and methods are similar to ones in topology, so if you can master this course better, you may perform excellently in topology.
Similar to topology, here are two notes, and one focuses on the definitions and another focuses on the theories in functional analysis. I believe these notes can help me remember them effectively and they really worked. So, just try to understand such theories and definitions and then remember them, practice them.
Main Definitions of Functional Analysis
Main Theories and their proofs of Functional Analysis