/sci/ - Science & Math

How does one begin to study higher-level mathematics?

I'm a chemical engineering undergraduate who has a solid understanding of calculus, differential equations, statistics and most things relevant to the discipline. I've always had an interest in pure mathematics.

Just doing some basic research on google doesn't leave me with much. There are a ton of mathematical structures and subfields to study, and I'm not sure where to start. I would be doing this in my free time, unfortunately I can't take any courses in this vein for electives.

What do, and where should I start? Help me /sci/entists.