This textbook on financial markets has two purposes: one is to introduce students to the latest theory of financial markets, and the other is to explain the advanced mathematics that is the language of this theory. It requires students to have a familiarity with the elementary ideas of ordinary calculus, linear algebra, probability, and microeconomics. The theory in the book is the basis for some very successful applications to a large and growing segment of financial markets: futures markets in commodities, interest rates, and stock indexes; and the options markets in the same areas.