This is an introductory course on Functional Analysis. We will start with a review of metric spaces, then we cover normed and Banach spaces and their operators as well as their duals. We study structure of Hilbert spaces and then we look at linear bounded operators of them and see basic results. The Hahn - Banach Theorem, Open Mapping and Closed Graph Theorems and Uniform Boundedness Theorems and their applications will be among the topics we cover in this course.