The notion of modular symbols was first introduced by Manin. We state some basic results which relate modular symbols to special values of L-functions and p-adic L-functions. We give Greenberg and Stevens construction of an overconvergent modular symbols which is a measure valued cohomology class attached to a Hida family of modular forms with certain interpolation properties. We will construct the Mazur-Kitagawa two variable p-adic L-function from the overconvergent modular symbol.