TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Battery: The lithium ion secondary battery comprises an inorganic substance comprising a lithium ion conductive crystal contained in a positive and/or a negative electrode; and is free of pores or a crystal grain boundary that impedes ion conduction. Preferred Components: The inorganic substance has a particle diameter less than or equal to one-fifth of the particle diameter of an active material of the positive and/or negative electrode; and is contained in 2 - 35 mass.% of the active material of the positive and/or negative electrode comprising the inorganic substance.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The inorganic substance that constitutes the powder of the inorganic substance is free of pores or a crystal grain boundary that impedes ion conduction. The powder of the inorganic substance has ion conductivity of greater than or equal to 10-4 Scm1; and an average particle diameter of less than or equal to 9 microns. The inorganic substance comprising the lithium ion conductive crystal is a lithium ion conductive glass-ceramic. The powder of the inorganic substance has, as a predominant crystal phase, a crystal phase of Li1+x+yAlxTi2-xSiyP3-yO12. The inorganic substance comprises (mol.%): Li2O (12 - 18), Al2O3 + Ga2O3 (5 - 8), TiO2 + GeO2 (35 - 45), SiO2 (1 - 10), and P2O5 (30 - 40); or comprises (mass.%): Li2O (3 - 10), Al2O3 + Ga2O3 (5 - 20), TiO2 + GeO2 (25 - 40), SiO2 (0.5 - 8), and P2O5 (40 - 55).x and y=0 - 1.Preferred Electrolyte: The solid electrolyte has a thickness of 20 - 60 microns; has an ion conductivity of greater than or equal to 10-5 Scm1; and comprises (mass.%): powder of the inorganic substance (50 - 95) and polymer (5 - 40).    TECHNOLOGY FOCUS - POLYMERS - The polymer has an ion conductivity of greater than or equal to 10-8 Scm1. EXAMPLE - A glass-ceramic of formula Li1+x+yAlxTi2-xSiyP3-yO12 (where x is 0 - 0.4, and y is 0 - 0.6), and a copolymer of polyethylene oxide and polypropylene oxide added with lithium tetrafluoroborate as a lithium salt were mixed uniformly at a ratio of 80:20 in an ethanol solvent and the mixture was coated on a PET film which had been applied with a treatment for releasing and than dried. Another PET film that had been applied with a treatment for releasing was adhered to the solid electrolyte thus obtained. The composite electrolyte was then heated at 150degreesC and was pressed by a roll press to remove bubbles remaining in the composite electrolyte. Then, the PET films on both sides of the solid electrolyte were stripped off. The solid electrolyte sheet obtained had thickness of 40 microns. By holding this solid electrolyte with a pair of stainless steel sheets and a specimen for measuring lithium ion conductivity was prepared using these stainless steel sheets as electrodes. A control example was prepared similarly without adding the lithium salt. The impedance of the test and control specimens at 25degreesC was measured for calculating ion conductivity. The ion conductivity (Scm1) for test/control was 1.3x10-4/7x10-9, respectively.