Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

From the reviews: "A prominent research mathematician and a high school teacher have combined their efforts in order to produce a high school geometry course.

The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa.

Inside PFTB ("Proofs from The Book") is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways.