This book is an introduction to the physics of elementary excitations in condensed matter with emphasis on basic concepts and their mathematical representations. The nature of the book is mainly determined by the fact that it was originally written, in Japanese, as one volume of Iwanami Series of Fundamental Physics supervised by Professor H. Yukawa. Our task was to portray the theory of condensed matter from a unified point of view for the student looking for his own research field and also for more senior readers interested in fundamentals of contemporary physics. As our point of view, we chose the concept of elementary excitation, which we believe to be one of the most fruitful concepts discovered by the quantum theory of matter. The present English edition has been translated by the authors themselves from the second, revised Japanese edition published in 1978, six years after publication of the first edition. In translating, we have introduced no major modifications; only the list of references has been made more suitable to overseas readers. In the English as well as in the Japanese editions, Chaps. 1,4, and part of 6 were written by Nakajima, Chaps. 2, 5, and 7 by Toyozawa, and Chaps. 3 and part of 6 by Abe. Finally we should like to thank Professor P. Fulde for kind help and Dr. H. Lotsch, SpriIiger-Verlag, for patient cooperation in making this English edition a reality.