I've recently become interested in various types of maths, and I was wondering if the community had any good book suggestions. I'm looking for any good intro to graph, set, or group theory. Any other book recommendations about more unique maths would be great. Thanks for the help everyone.

"Abstract Algebra" by Dummit and Foote is the industry standard undergrad level text on algebra. It's a big exhaustive encyclopedia of the basics of groups, rings, modules, and all sorts of good stuff, and is very readable. The first 20-25% of the book covers groups. Unless you're an algebraist, it's probably the only algebra text you'll ever need.

I'm pretty sure "Graph Theory" by Diestel is more or less the standard introductory graph theory text, although I've never read it. I didn't learn any graph theory until after starting grad school, from Bollobas' excellent "Modern Graph Theory", but that's almost certainly too involved for a first text.

For set theory, again, the only book I know well is Jech's massive tome, which is again, way too advanced, but I would think that either of "Naive Set Theory" by Halmos or "Introduction to Set Theory" by Hrbacek are fine. I think "The Joy of Sets" by Devlin is a common choice for undergrad classes. "Set Theory and the Continuum Hypothesis" by Cohen is excellent as well, but might be a tad on the advanced side.

If you're interested in number theory:
"An Adventurer's Guide to Number Theory" by Richard Friedberg is great. I also recommend "Excursions in Number Theory" by C. Stanley Ogilivy and John T. Anderson.

For a great tour of most of modern mathematics, I suggest "Concepts of Modern Mathematics" by Ian Stewart. This is reprint of a book that was originally published in 1975 and revised in 1981. Stewart used the term "Modern" to mean the last 100 years, but I think this book spans a longer period than that. Yes, the book is "old" but I think well-written math books age very slowly.

Finally, not a book but:
Wolfram MathWorld
http://mathworld.wolfram.com

If you are interested in Origami, I would recommend Origami Design Secrets: Mathematical Methods for an Ancient Art. I own and have read most of the first edition, and quite like the way it presents some of math underlying complex origami designs. There is a second edition that I hear is a worthwhile improvement, but I have yet to order it on account of my vision degrading to a point that reading is impossible.