In this chapter, we study functions, called multiplicative functions, that are defined on integers. These functions have the property that their value at the product of two relatively prime integers i...In this chapter, we study functions, called multiplicative functions, that are defined on integers. These functions have the property that their value at the product of two relatively prime integers is equal to the product of the value of the functions at these integers. We start by proving several theorems about multiplicative functions that we will use later. We then study special functions and prove that the Euler ϕ -function that was seen before is actually multiplicative.