Background: I am currently studying physics and except for high school mathematics I have experience with linear algebra, single- and multivariable calculus, differential equations (mostly ODE's, but I have some limited experience with PDE's), and some transform theory. I also know some basic set theory, graph theory and really simple enumerative combinatorics. I am interested in higher mathematics such as abstract algebra, the more rigorous (than calculus) analysis and topology, according to what I know about them.
I saw a recommendation on Hacker News, for three books about exactly these areas of mathematics and according to the post, the books are "hardcore" in the sense that they are hard to go through, but provide many rewards for doing it. This is exactly what I want. What do you think, are the books to be recommended?
Also, which area would you recommend that I start with?