The direct and inverse Sturm-Liouville problems with the discontinuity conditions involved spectral parameter at finite interior points inside a closed interval are considered in this talk. We give a self-adjoint operator-theoretic formulation for this problem, and its expansion theorem by reference to the self-adjointness of the operator. Furthermore, we give its asymptotic behavior of the solutions and eigenvalues for this problem and provide several uniqueness results for the inverse spectral problems.