I'm studying very basic Lie group theory by working through John Stillwell's Naive Lie Theory. The end-goal in this direction is to acquire the basics of modern differential geometry. If I make it to the end of this book, I've got Janich's Vector Analysis (differential manifolds, differential forms, Stokes' theorem in the modern setting, de Rham cohomology) and Loomis & Sternberg Advanced Calculus (all this and more, starting from basic linear algebra and multivariable calculus in a principed way). Not decided yet which of them I'll try to work through or both.

Independently of this, I would like to refresh probability and acquire statistics in a mathematically rigorous way. I tried Wasserman's All of Statistics that is sometimes recommended, but it's too dry and unmotivating for me. I like the look of David Williams's Weighing the Odds, which seems to be both suitably rigorous and full of illuminating explanations, but I haven't really tried reading it yet.