All but the most straightforward proofs are worked out in detail before being presented formally in this book. Thus most of the ideas are expressed in two different ways: the first encourages and develops the intuition and the second gives a feeling for what constitutes a proof. In this way, intuition and rigour appear as partners rather than competitors. The informal discussions, the examples and the exercises may assume some familiarity with calculus, but the definitions, theorems and formal proofs are presented in the correct logical order and assume no prior knowledge of calculus. Thus some basic knowledge of calculus is blended into the presentation rather than being completely excluded.