This book serves as a valuable resource for mathematics and science teachers at secondary school level, teenagers and parents. It contains written versions of Royal Institution masterclasses on a wide selection of topics in pure and applied mathematics. The masterclasses are a popular program of advanced study conducted each year for mathematically talented university-bound British youth. They serve as a unique introduction to the kinds of topics found at the undergraduate level, yet presented in a manner that is meant to stimulate interest and challenge young minds. Topics include chaos theory, meteorology, storage limitations of computers, population growth and decay, as well as the mechanics of dinosaurs. The book is well-illustrated, easy to read, and contains worksheets with interesting problems (and solutions). The emphasis throughout is on enjoying the challenge of mathematics.