A self-contained introductory review is presented of the HiggsKibble mechanism, which included the gauge theory, spontaneous symmetry breaking, the Goldstone theorem, etc.. The Higgs-Kibble mechanism and its relevant problems are reexamined and clarified with some comments. All the matters associated with the spontaneous broken symmetry are investigated on the basis of the axiomatic quantum field theory of Wightman. The S-matrix in the Higgs-Kibble mechanism is proved to be gauge invariant, and the indefinite metric formalism is required to decompose the states into the transverse parts and the other parts, i.e., $\psi=\psi_T\times\psi_o$, for any massless or massive vector field. The state, $\psi_o$ consists of the Goldstone bosom and the ghost which are unphysical, and so any physical trace of them can not appear. The asymptotic behavior and the unitarity of the R-gauge in the Higgs-Kibble mechanism are discussed by using the Yang-Feldman formalism on the basis of the indefinite metric quantum field theory.