Here I'll introduce some books, and (maybe) lecture notes, not oriented to promote any specialized topics in mathematics, but a necessary knowledge base that I think is good for pre-freshman in university-level mathematics.
Furthermore, I'll continuously update this post, unless it is disagreed.
How to study for a mathematics degree
Lara Alcock, $OUP, 2013$. Though the name of the book is not as interesting, it is, definitely, a good way to introduce one to a thinking style of advanced mathematics.
Terence Tao, $Springer, (III\ Edition)2016$. A really good book in introducing the way of thinking in a constructive, based-on-axiom ways. No need further introduction, as the name of its author is enough to explain. You may also find Tao's lecture notes here at UCLA.
Mathematical Analysis I
Vladimir A. Zorich $Springer, 2002$. My self-introducing book during my first year of high school, while I've finished all A-level syllabus. It gives a relatively fine way of teaching, with a level of difficulty, and also thanks to the use of logical notation by Zorich, it may give some awkwardness when first seeing it. But if you have familiarized with it, and also, trained yourself with the exercises, it must give you a better and wider view for your future studies, at least for myself.
Some other lecture notes
Calculus (Preliminary level): $Oxford$
Calculus (differential equation): $Oxford$
Calculus (vector calculus):
Group theory: $Cambridge$