Considering a PhD and/or a career in academia?
I recommend reading Katabasis by R.F. Kuang and Principle of Mathematical Analysis by Walter Rudin
Want to get a taste of first year PhD level econometrics cousework?
Try the first 10 chapters in Bruce Hansen's Econometrics and some topics of interest from Applied Causal Inference Powered by ML and AI by Victor Chernozhukov, Christian Hansen, Nathan Kallus, Martin Spindler, and Vasilis Syrgkanis
Interested in becoming an econometrician?
Here are some lecture videos, notes, and textbooks that I found rather helpful for my line of work.
Lecture videos on Probability Theory and Stochastic Processes by Todd Kemp
Advanced Probability for Statisticians and Empirical Process Theory by Kengo Kato
High-Dimensional Probability by Roman Vershynin
U-Statistics: Theory and Practice by A. J. Lee
Quantile Regression by Roger Koenker
Large Sample Estimation and Hypothesis Testing (Handbook Chapter) by Whitney K. Newey and Daniel McFadden
It is rare to feel completely mathematically prepared for research, as the demands of new projects are often inherently unpredictable. At a certain threshold of foundational knowledge, rather than aimlessly studying more advanced mathematical topics, a more effective approach is to begin working on a project and acquire the necessary mathematical tools as the need arises.