Problems in Mathematics

try 50 Challenging Problems In Probability by Mosteller. it starts pretty basic and works up slowly to a good foundation for learning probability theory in a rigorous way using very neat problems.

https://www.amazon.com/Challenging-Problems-Probability-Solu...

A link normalizing addon would be cool, add some safe rel tags and a setting to prefer new tab/same tab

Those were all standard topics, generally in years 2-3, at my undergrad program circa 2006.

I took all of those except module theory in my undergrad math classes back in the early 90s. However some of them (for example Galois theory) were optional courses.

All of those are typically in a single undergraduate course on abstract algebra. Depending on the specific course you might only touch on Galois theory and modules, but you'll definitely get exposure to both. Most undergraduate textbooks will have a chapter/section devoted to each of those topics.

Were you a math major?

Almost every math major covers an intro to Group Theory, Ring Theory, Field Theory. That's just about all you can do in pure math immediately after Linear Algebra (except number theory and some probability), and the foundation for almost everything you'd try.

If "applied math" was not separated from "pure math" in your school, and you did non-math electives after the minimum core math classes, then you might avoid these topics in favor of a broad curriculum of differential equations, graph theory, probability, and such.

Galois Theory, or Module Theory would be electives or touched on in high-expectations program.