The objective of this chapter is to discuss the major properties of Fourier Transform for preparation of the subsequent chapters. Fourier Transform has some important properties. These properties are very useful for understanding much of the remainder of this book, such as filtering theory and its applications, the effect of finite sampling, and window functions. We discuss the major properties, but some have more important applications than others, depending on the question at hand. Their usage, if applicable, will become clear in later chapters. This chapter is theoretical and does not have MATLAB implementation, which is deferred to later chapters where relevant.