"The author studies specifically some relevant aspects of the spectral theory for block operator matrices from a new standpoint and incorporates recent results of his own works. ... the book provides a large variety of important applications in many branches of mathematics as well as physics, biology, and some open questions are given, too. This book may be of interest for both experienced researchers and graduate students." (Carlos R. Carpintero, zbMATH 1354.47001, 2017)