[robpal]

My experience from a decade of doing professional maths is that there are no shortcuts. You only learn maths by doing hundreds (thousands) of exercises, both mundane and more exctiting.

Also, the concepts "mature" in the brain. I remember sleepless nights in the first year of undergrad spent on understanding the details of the proof of the Jordan decomposition and a few years later (when studying algebraic groups) it all felt trivial.

There's no shortcut to understanding maths, just a lot of time spent in solitude trying to make sense of all these abstract concepts (and they DO make sense).

[Chris2048]

I think there is a shortcut: use examples (a "domain") rather than starting with theory. learning something purely in the abstract is easy to forget.