Since you are student at university, I would emphasize, in addition to your own reading: Talk to people who already understand the area. In office hours with yo

Since you are student at university, I would emphasize, in addition to your own reading: Talk to people who already understand the area. In office hours with your professor, or grad students, or even more senior undergrads. Just hang out with people who know more than you and talk to them about math, not even necessarily just analysis. It may not be the specific things they teach you, but rather the modes of thinking that are obvious after the fact but impenetrable before.