The present invention relates to a solid electrolyte comprising a first polymer which is a polyvinyl acetal or polyvinyl acetate, or a copolymer having vinyl acetal and/or vinyl acetate units, doped with a sodium or lithium salt. The present invention also relates to method of forming a solid electrolyte comprising the first polymer and LAGP ceramic into a membrane. The solid electrolyte may be used as an ionically conductive membrane in a battery such a Li-air battery.