From the construction of primitive tribal huts to the design of technologically advanced high-rise buildings, architects have relied on and been inspired by mathematics. This chapter introduces and categorizes three types of applications of mathematics in architecture. The first comprises aesthetic applications, which are visible or expressed in a building. The second are practical applications that provide support for the creation of a stable, durable, and functional building. The last category comprises analytical applications that reveal various previously invisible properties of a building. Using this framework, the chapter examines major architectural themes, spanning historically from Ancient Egypt to the present day, and in scope from number mysticism to advanced computational analysis. Through this process, the chapter investigates the rich, symbiotic relationship between architecture and mathematics, offering a series of mechanisms for understanding the many ways they are connected.