I am looking for a rigorous math textbook that introduces many subjects in university (undergraduate) math. One book that seems to meet this criteria is Alan Beardon's Algebra and Geometry but I haven't been able to preview it properly so I would appreciate a short review if you have read it. There are also these engineering/"math4physicists" type books that do this but unfortunately not rigorously. Any others apart from Beardon?
Note: I hope this question is defined enough so as not to get deleted, but if not please let me know how to improve it before voting to close. My questions get closed far too often and I still don't know the problem.
Thanks