The objective of this book is to give a self-contained presentation to the theory underlying the valuation of derivative financial instruments, which is becoming a standard part of the toolbox of professionals in the financial industry. Although a complete derivation of the Black-Scholes option pricing formula is given, the focus is on finite-time models. Not going for the greatest possible level of generality is greatly rewarded by a greater insight into the underlying economic ideas, putting the reader in an excellent position to proceed to the more general continuous-time theory. The material will be accessible to students and practitioners having a working knowledge of linear algebra and calculus. All additional material is developed from the very beginning as needed. In particular, the book also offers an introduction to modern probability theory, albeit mostly within the context of finite sample spaces. The style of presentation will appeal to financial economics students seeking an elementary but rigorous introduction to the subject; mathematics and physics students looking for an opportunity to become acquainted with this modern applied topic; and mathematicians, physicists or quantitatively inclined economists working in the financial industry.