Are you looking for exercises to prepare for exams, materials for tutorials, or examples for a lecture on advanced calculus? In this comprehensive book, you will find a wide variety of tasks - from abstract proofs to theoretical and applied examples, as well as concrete calculations. Detailed solutions are provided for each task to help you verify your work. Thus, this work is the ideal companion for both students and instructors of mathematics. The compilation of exercises was created during the author's corresponding lectures at the University of Siegen from 1993 to 2013.