TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Composition: The rechargeable lithium metal or lithium-ion cell is a lithium-sulfur cell or lithium-ion sulfur cell containing a sulfur cathode.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The anode active material is lithium metal, lithium metal alloy, mixture of lithium metal or lithium alloy with lithium intercalation compound, lithiated compound, lithiated titanium dioxide, lithium titanate , lithium manganate, lithium transition metal oxide and/or lithium-titanium oxide (Li4Ti5O12). The anode active material includes silicon, germanium, tin, lead, antimony, bismuth, zinc, aluminum, nickel, cobalt, manganese, titanium, iron, cadmium and/or their lithiated compound, or alloys or intermetallic compounds of silicon, germanium, tin, lead, antimony, bismuth, zinc, aluminum or cadmium with other elements, and their lithiated compound, or oxide, carbide, nitride, sulfide, phosphide, selenide or telluride of silicon, germanium, tin, lead, antimony, bismuth, zinc, aluminum, nickel, cobalt, manganese, titanium, iron, cadmium or their composite material or lithiated compound, or salt and hydroxide of tin and/or its lithiated compound, or carbon or graphite material and/or its pre-lithiated compound, when the cell is lithium-ion cell or lithium ion-sulfur cell. The cathode comprises an integrated nanostructure of electroconductive nano-filaments which are interconnected to form a porous network of electron-conducting paths comprising pores with a size less than 100 nm, and powder or coating of the cathode active material provided in the pores or deposited on nano filament surface. The filaments comprise electroconductive material. The electroconductive material is electro-spun nano fiber, vapor-grown carbon or graphite nano fiber, carbon or graphite whisker, carbon nanotubes, carbon nanowires, nano graphene sheet or platelet, metal nanowires, metal-coated nanowires or nano fiber and/or conductive polymer-coated nanowires or nano fiber. The nano graphene sheet or platelet is single-layer or few-layer pristine graphene, reduced graphene oxide, graphene oxide, hydrogenated graphene, nitrogenated graphene, doped graphene and/or chemically functionalized graphene. The cathode has active material utilization rate of 90% or more. The cathode active material is transition metal dichalcogenide, transition metal trichalcogenide and/or transition metal oxide, preferably titanium sulfide, tantalum sulfide, molybdenum sulfide, niobium selenide, manganese oxide, cobalt oxide, iron oxide and/or vanadium oxide. The vanadium oxide in the cathode active material is vanadium oxide (VO2, V3O8, V2O5, V4O9 or V6O13), lithium vanadium oxide (LixVO2, LixV2O5, LixV3O8, LixV3O7, LixV4O9 or LixV6O13, where x is more than 0.1 to less than 5), or their doped compound or derivative. The cathode active material contains layered compound of formula: LiMO2, spinel compound of formula: LiM2O4, olivine compound of formula: LiMPO4, silicate compound of formula: Li2MSiO4, tavorite compound of formula: LiMPO4F and/or borate compound of formula: LiMBO3, where M is transition metal or mixture of multiple transition metals.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Composition: The concentration of ionic liquid solvent (S1) is more than 10M. The ionic liquid solvent (S1) is a room-temperature ionic liquid having cation and anion. The cation is tetraalkylammonium, di-, tri-, or tetra-alkylimidazolium, alkylpyridinium, dialkylpyrrolidinium, dialkylpiperidinium, tetraalkylphosphonium and/or trialkylsulfonium. The anion is selected from tetrafluoroborate, tetracyanoborate, methyltrifluoroborate, Vinyltrifluoroborate, trifluoromethyl trifluoroborate, pentafluoroethyl trifluoroborate, (heptafluoro-n-propyl)trifluoroborate, (nonafluoro-n-butyl)trifluoroborate, hexafluorophosphate, trifluoroacetate, trifluoromethane sulfonate, bis(trifluoromethylsulfonyl)imide, trifluoromethylsulfonyl, trifluoromethyl ketone-trifluoromethylsulfonyl imide, bis(fluorosulfonyl)amide, tricyanomethanide, dicyanamide, thiocyanate, selenocyanate, copper chloride and/or aluminum chloride. The electrolyte further contains a solubility-promoting agent. The content ratio of solubility-promoting agent and ionic liquid (I1) is less than 1/9. The solubility-promoting agent includes an organic liquid or an ionic liquid (I2). The solubility-promoting agent is ether-based solubility-promoting agent or carbonate-based solubility-promoting agent. The ether-based solubility-promoting agent includes 1,3-dioxolane, 1,2-dimethoxyethane, tetraethylene glycol dimethyl ether, poly(ethylene glycol)dimethyl ether, diethylene glycol dibutyl ether, 2-ethoxyethyl ether, sulfone, sulfolane and/or their carbonate. The carbonate-based solubility-promoting agent includes ethylene carbonate, dimethyl carbonate, methyl ethyl carbonate, diethyl carbonate, ethyl propionate, methyl propionate, propylene carbonate, gamma -butyrolactone, acetonitrile, ethyl acetate, propyl formate, methyl formate, toluene, xylene, methyl acetate, fluoroethylene carbonate, vinylene carbonate and/or allyl ethyl carbonate. The lithium salt is lithium perchlorate, lithium hexafluorophosphate, lithium borofluoride, lithium hexafluoroarsenide, lithium trifluoro-metasulfonate, lithium bis(trifluoromethylsulfonyl)imide, lithium bis(oxalato)borate, lithium oxalyldifluoroborate, lithium oxalyldifluoroborate, lithium nitrate, lithium fluoroalkyl phosphate, lithium bisperfluoroethysulfonylimide and/or ionic liquid lithium salt. The ionic liquid (I1) is mixed with an organic solvent-based solubility-promoting agent. The organic solvent-based solubility-promoting agent includes ethylene carbonate, dimethyl carbonate, methylethyl carbonate, diethyl carbonate, ethyl propionate, methyl propionate, propylene carbonate, gamma -butyrolactone, acetonitrile, ethyl acetate, propyl formate, methyl formate, toluene, xylene, methyl acetate, fluoroethylene carbonate, vinylene carbonate, allyl ethyl carbonate, 1,3-dioxolane, 1,2-dimethoxyethane, tetraethylene glycol dimethylether, poly(ethylene glycol)dimethyl ether, diethylene glycol dibutyl ether, 2-ethoxyethyl ether, sulfone and/or sulfolane. The ratio of ionic liquid solvent (S1) and organic solvent is 10:1 or more.