I'm fairly well-versed in calculus but I would like to explore beyond calculus. I have looked into the basics of some topics in higher mathematics such as group theory and abstract algebra and they intrigue me. I am wondering if there are any recommended methods or resources I should use to learn more about these topics. And is there any recommended starting point?
These free video lectures by B. Gross at Harvard are outstanding:
They even have a set of notes taken by a very capable grad student.
Check out saylor.org. It's a free website with a pretty full curriculum of undergraduate math courses and each course has readings, videos, problem sets, etc. Really everything you need to self-study if you don't have the desire or opportunity to enroll in an actual course. Good luck!