Large part of the behavior of the world around us can be described with the help of functions. These functions by themselves are usually too complicated to understand, but we can already learn a lot from approximations. This is where mathematical analysis comes in: Mathematical analysis is about making and proving rigorous statements about the approximate behavior of functions. In this course Analysis 1, we will work our way up to a rigorous statement that expresses that close to a certain input point, a function can be approximated by a constant function. This property, called continuity, is often a very desirable property for a function to have.