The Spirit of Mathematics brings to life the most elementary parts of arithmetic, algebra, and geometry in a new way. It sets out problems and draws out the wonder and 'magic' of finding their solutions with an infectious enthusiasm. Acheson packs a remarkable amount of surprising mathematics into this short work. Given the author's own specialisms (mainly fluid dynamics and astrophysics), it is good to see a substantial emphasis on the use of algebra in applied mathematics. There are stimulating chapters on passing trains, crossed ladders, rollercoaster dynamics and tuning a guitar. The book ends with some paradoxes involving infinite series and the AM-GM inequality. I can recommend it thoroughly.