This book concerns the topics which every undergraduate mathematics student "should" know but has probably never encountered. These topics are not the ones which dominate every syllabus, but those magnificent secrets that are beautiful, useful and accessible but which are inexplicably hidden away from the mainstream curriculum. Each chapter of this book concerns a different topic which students will almost certainly be unfamiliar with. Written in a lively, conversational style, by the end of each section the reader should feel equipped with the knowledge to explore the area more fully elsewhere.