One of the key decisions that must be made by an author who is writing in the area of derivatives concerns the use of mathematics. If the level of mathematical sophistication is too high, the material is likely to be inaccessible to many students and practitioners. If it is too low, some important issues will inevitably be treated in a rather superficial way. I have tried to be particularly careful about the way I use both mathematics and notation in the book. Non essential mathematical material has been either eliminated or included in end-of-chapter appendices and the technical notes on my website. Concepts that are likely to be new to many readers have been explained carefully and many numerical examples have been included.