Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. it is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. this book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics that may be attractive to those interested in mathematics.