In the spirit of making this book reasonably self-contained, certain topics that may be required in understanding the foundation and the applications of quantum mechanics are discussed. Foremost are the definition and properties of the complex numbers, such as De Moivres theorem and Eulers identity. Trigonometry and vector analysis are the necessary topics for almost any discussion of physical phenomena. In this chapter these topics are discussed to the extent that makes their use in subsequent chapters quite natural and normal. Another topic that reverberates throughout this book due to the nature of quantum mechanics is probability theory. Here the main ideas of probability theory are presented that should be sufficient for an understanding of the topics discussed in this book.