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In this book, recent progress in batteries is firstly reviewed by researchers in three leading Japanese battery companies, SONY, Matsushita and Sanyo, and then the future problems in battery development are stated. Then, recent development of solid state ionics for batteries, including lithium ion battery, metal-hydride battery, and fuel cells, are reviewed. A battery comprises essentially three components: positive electrode, negative electrode, and electrolyte. Each component is discussed for the construction of all-solid-state Batteries. Theoretical understanding of properties of battery materials by using molecular orbital calculations is also introduced.