There are many texts on mathematics for economists but virtually none that seek to present financial theory and the relevant areas of economics to mathematically mature readers at an introductory level. The present text seeks to remedy that deficiency while at the same time giving a challenging view of a subject where recent events have led to a widespread search for new approaches that move away from orthodox and traditional perspectives. So this is as much a book that asks as a book that tells. I am convinced that financial theory can be placed on a much surer footing than it is at present, but traditional economics persistently fails to ask the right questions. Only since the present Financial Crisis has it finally come to be widely accepted that methods that work for goods markets give quite the wrong impression for asset markets, and if we're to try to understand the instability of the system we all have to live in, it's asset markets that must be understood. There's a lot of work under way in this direction already, but I would hope that by asking the questions I'm asking and reviewing how far established methods go to answering them and how far they don't I can give this work a boost.