Not a mathematician, but have spent some time self-learning math. I have not gone through the following books entirely, however I've used them when needed to learn or clarify a concept:
> Group Theory - I would look for a good abstract algebra book that also covers groups, such as A First Course in Abstract Algebra, Fraleigh or Basic Algebra, Knapp. Another popular recommendation is Abstract Algebra, Dummit and Foote.
> Topology I think you should first look at a real analysis course and understand metric space topology for Euclidean spaces. If you have taken calculus, you can try and go through Baby Rudin. For topology specifically you can look into Munkres or Introduction to Topological Manifolds, J Lee.
> Measure Theory T. Tao has a good book on this topic.
> Differential Geometry Introduction to Smooth Manifolds by J Lee
> Probability Probability Theory, Achim Klenke
> Game Theory Game Theory by Maschler, Solan & Zamir