I tried once to read Terence Tao's Analysis I [2], it's really good but my main problem was that I wasn't able to know if my proofs are correct when I do an exercise. So maybe the solution is to get a teacher.
[1]: https://en.wikipedia.org/wiki/Principles_of_Mathematical_Ana...
I have used Google's "AI Overview" and "AI Mode" profitably to have it explain new concepts to me in simple terms and also have had it verify my own understanding of something. The reason i prefer it is because it is a search-driven reasoning engine and thus gives references (in tooltips) directly to the latest sources/articles on the web from which it synthesized its answers.
As an example, there can be "AI Librarian" and "AI Reasoner" personas which set boundaries for what each should do. The former is for organization of data with citations and synthesizing answers objectively with simple explanations while the latter is for more detailed deep dives with logical analysis and thinking.
Note however, that persona's must be distinct in terms of data usage and not role-playing which is largely ineffective.
I haven't tried it with analysis, but I did for linear algebra. It would quickly spot flaws in my proof.