A concise and friendly introduction to topics in arithmetic, algebra and basic probability that are usually covered at high school level. The aim is to take the mystery out of the various rules and formulas that students encounter in their textbooks, and help them to reason independently and correctly about the properties of mathematical objects. It is the author's conviction that most young people who dislike mathematics do so out of a misunderstanding of what the subject is really about. Written for the benefit and understanding of school students in the 12-16 age group worldwide.