At first, this book looks suspiciously like a textbook, complete with hundreds of diagrams and pages full of mathematical notation. On a closer reading, however, one discovers that the book is something entirely different and far more remarkable. This volume is written to explore the elegant connection between mathematics and the world.

Beginning with the deceptively simple geometry of Pythagoras and the Greeks, the author guides readers through the fundamentals — the incontrovertible bricks that hold up the fanciful mathematical structures of later chapters. From such theoretical delights as complex-number calculus, Riemann surfaces and Clifford bundles, the tour takes us quickly on to the nature of space-time.

Those who work their way through these initial chapters will find themselves rewarded with a deep and sophisticated tour of the past and present of modern physics.

Bulk of the book is devoted to quantum physics, cosmological theories (including Penrose’s ideas about string theory and universal inflation), and what we know about how the universe is held together.

For physicists, mathematicians and advanced students, this book is an essential field guide to the universe. For amateurs, it is a project to tackle a bit at a time, with unimaginable intellectual rewards.