I got a master's in engineering, so a lot of the foundations stuff is missing. Basically the math there is all very applied stuff, not a lot of elegance and overview.
Another intro book I thought of was Peter Eccle's introduction to mathematical reasoning. Might be worth looking at.
If you want a nice leisurely introduction to groups Nathan Carter's Visual group theory is nice.
I got a lot of use out of the princeton encyclopedias of math. Dont expect for them to really teach you anything, but the articles are nice for seeing whats out there.
Definitely try to learn basic analysis and algebra. I dont think any book I know is amazing, but basically any will do the job.
Importantly, dont be afraid to try to learn something out of your depth. In fact I think its important to try! If something really grabs you, try to read more and backfill what you don't know.