The basic results that are covered in this course (an introduction to functional analysis) can be found in N+1 textbooks and online notes. Similarly for some standard examples and applications. Other examples and applications that will be presented cannot be found in any single source, so the students are advised to keep notes. The homework assignments are also taken from various sources, but they will be posted on the class web page. Part II of this course (distributions, Sobolev spaces, fundamental solutions of PDEs, ...) will be taught by Prof. Arbogast in the Spring 2009, using an updated version of his 2005 notes with J. Bona. These notes can be purchased at the Welch Copy Center. They also cover introductory functional analysis and thus can be useful for the current course as well; especially for those students that plan to take Prof. Arbogast course, where the notes will be mandatory.