The Art of the Infinite
This is the kind of book I wish I’d read 20 years back.
The Kaplans cover a lot of ground, so the book is densely packed with remarkable insights. Although most of the topics (algebra, geometry) were covered in my school syllabus in my younger days, the difference is in how it bridges vast areas of mathematics together.
A seemingly insurmountable problem is shown first. Then some remarkable piece of magic happens. And the clouds clear and light shines through.
A book like this gives a glimpse of the awe-inspiring structure and symmetry in the Universe that mathematicians create in their minds.