Symmetric periodic solutions of the Hill's problem

A survey of previously studied and new families of symmetric periodic solutions of the Hill's problem in terms of its generating solutions is given. For any generating solution in the form of generating sequence formulated and proven statements that define type of symmetry, global multiplicity and asymptotic of initial conditions of the family defined by this generating sequence. An algorithm for investigation of the family of symmetric periodic solutions that defined by its generating sequence is provided. With the help of this algorithm new families of periodic solutions of the Hill's problem were found and investigated. These families have orbits that overflying libration points $L_1$ and $L_2$ in definite order.