NOVELTY - Lithium secondary battery comprises a positive electrode (116), a negative electrode (118) and an electrolyte comprising a polymerizable compound or a polymer, where the polymerizable compound comprises a compound having an aromatic functional group and a polymerizable functional group and a compound having a complex-forming functional group forming a complex with a metal ion and a polymerizable functional group, and the polymer has the complex-forming functional group, the aromatic functional group and a residue of the polymerizable functional group.    USE - The lithium secondary battery is useful in e.g. a notebook computer and a cell phone.    ADVANTAGE - The lithium secondary battery has: suppressed gas generation and suppressed decrease in battery capacity during high temperature storage; and improved electrochemical stability.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for:    (1) the polymer comprising poly(1-vinyl-naphthalene) of formula (I) or poly(2-vinyl-naphthalene) of formula (II), where a, b and c are expressed in mole%;    (2) an electrolytic solution for the lithium secondary battery, where the electrolytic solution comprises the polymerizable compound or the polymer;    (3) a positive electrode protective agent for the lithium secondary battery, where the polymerizable compound or the polymer is used as an active component; and    (4) manufacturing the polymer comprising: preparing a mixture comprising the polymerizable compound having the aromatic functional group and the polymerizable functional group, and the polymerizable compound having the complex-forming functional group forming complex with the metal ion and the polymerizable functional group; and polymerizing the polymerizable compounds.    R1 = H, hydrocarbyl, cyclic hydrocarbyl, aromatic group, (-OR), (-SR), (-COOR) or (-SO3R);    R2, R3, R4 = H or hydrocarbyl;    R = H, alkyl metal, alkaline earth metal or alkyl;    Y1 = complex-forming functional group forming a complex with a metal ion;    W1 = highly polar functional group having a functional group with high polarity;    a = greater than 0 and less than or equal to 100; and    b, c = greater than or equal to 0 and less than 100.    DESCRIPTION OF DRAWING(S) - The figure shows a cross sectional view of a lithium secondary battery.    Cover plate (113)    Positive electrode (116)    Separator (117)    Negative electrode (118)    Insulating body (123)