Any book on cryptography written for a more-or-less lay audience must inevitably face comparisons to *The Code Book*, written in 1999 by Simon Singh, the king of distilling complex subjects to a few hundred pages of understandable writing. While Singh’s book is a pretty thorough history of codes and codebreaking ((I will in this review unapologetically make no attempt to maintain any distinction between the terms code and cipher; cryptography, cryptanalysis and codebreaking, etc.)) through the centuries with plenty of the maths thrown in, *The Mathematics of Secrets* is tilted (and indeed titled) more towards a fuller explanation of the mathematical techniques underlying the various ciphers. Although Holden’s book follows a basically chronological path, you won’t find too much interest in pre-computer ciphers here: Enigma is cracked on page seventy, and the name Alan Turing does not appear in the book.