This book covers thematically organized applications and problems with complete solutions related to multidimensional integration theory, Fourier analysis, and complex function theory with applications. Introductions at the beginning of each lesson summarize the theoretical foundations for independently tackling the problems, and numerous illustrations aid in the visual understanding of the material. The application topics discussed here were not only significant for the historical development of classical analysis but are also timeless, making them helpful today for a deeper understanding and learning of advanced analysis. Thus, the book is aimed at readers who wish to be inspired by engaging application topics. Due to the systematic structure of the material, it is well-suited for use alongside the regular lecture cycle as well as for exercises and seminars as supplementary material.