Fundamental Concepts of Mathematics is the first of several volumes of a proposed series on fundamental mathematics which serve primarily as textbooks for students in preparation for the A-Level or other public examinations. However they go into more depth than what is required by these examinations, and contain topics that are useful but often omitted for lack of time in the undergraduate courses. Therefore the books of this series can also be used by university students as reference books for supplementary reading. Further volumes on topics in algebra, geometry and calculus are forthcoming. It is sincerely hoped that in their entirety they will ease the dire shortage of suitable textbooks for A-Level mathematics that has persisted over decades in Hong Kong.