This book is written for the New Senior Secondary Math Curriculum in Hong Kong. Its aim is to provide an alternative approach to learning mathematics, an approach more vigorous than that provided by most standard textbooks in Hong Kong. In this book, besides examples, which are similar to those found in standard textbooks, there are many definitions and theorems etc. Examples tell us how to do. To know what we are doing, we need definitions etc. To understand why we can use a certain method, we need theorems etc. Although, the concept of sets is not included in the math curriculum, it is used implicitly in the concept of domains (of functions) and that of events (in the topic of probability). For this reason, a brief introduction to set languange is given in the first part of Chapter 1.