This book describes why cobalt oxides have drawn much interest as functional materials and their peculiar physical properties partially originating from a rich variety of the valence and spin state of Co ions. In functional Co oxides, where the conventional one-electron approximation fails, the strong correlation between electrons plays a substantial role. The book starts with basics of condensed matter physics and advances toward the stage of strong electron correlation system. It further provides up-to-date information on topics such as huge thermoelectric power, superconductivity, solid oxide fuel cell, nanostructure effect, and so on. Among the transition metal oxides, copper and manganese oxides are known for superconductivity with high transition temperature and colossal magneto resistance, and numerous publications already exist on them. Cobalt oxides are generally recognized only as Li-ion battery materials, and the functionality and physics behind their peculiar physical properties are not summarized even in existing publications. The book focuses on functional cobalt oxides from basics to application along with recent progress through its topics, which will be of interest to a wide audience.