This book provides an exploration of the mathematics underlying the works of the Catalan architect Antoni Gaudi i Cornet (1852-1926). Illustrated by over 300 graphics and photographs, the text describes the applications of geometry that are found in Gaudí's buildings. The narrative is further enhanced by numerous ""Math Moments,"" highlighting the mathematics and mathematicians that come to mind when one observes Gaudi's creations. After an opening chapter giving a pictorial overview of Gaudi's work, the book covers topics from two- and three-dimensional geometry such as plane curves, ruled surfaces, ellipsoids, paraboloids, polygons, and polyhedra. Special attention is given throughout to Gaudi's magnum opus, the Basilica de la Sagrada Família. The book finishes with detailed appendices, including a brief biography of the architect as well as supplemental proofs and technical notes to develop ideas from the main text. Suitable for lovers of geometry or architecture, the modest prerequisites mean The Genius of Gaudi can also be used as a supplemental text for a geometry course at the high-school level and above. In addition, it may be enjoyed as a mathematical tour guide for anyone visiting the city of Barcelona.