Recent progress in batteries and future problems -- Recent development of amorphous solid electrolytes and their application to solid-state batteries -- Recent development of electrode materials in lithium ion batteries -- Construction of solid/solid interface between hydrogen storage alloy electrode and solid electrolyte for battery application -- Polymer solid electrolytes for lithium-ion conduction -- First principles calculations of lithium battery materials.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.