This third volume concludes our introduction to analysis by laying the groundwork for further study of the subject. Like the first two volumes, this one contains more material than can be covered in a single course. Therefore, it is important to make a suitable selection from the content when preparing lectures; the remaining part can be addressed in seminars or left for self-study. For a quick overview of this content, please consult the table of contents and the chapter introductions. This book serves as a background for other courses or for self-study. We hope that the numerous insights into advanced analysis will spark curiosity and invite students to further explore the beauty and scope of this branch of mathematics. In creating this volume, we have relied on the invaluable assistance of friends, colleagues, staff, and students. Special thanks go to Georg Prokert, Pavol Quittner, and Olivier.