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. 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.