A new effect between a superconductor with superconducting transition temperature T(,cs) and a normal metal N (T(,cn)) (or another superconductor with T(,cn) < T(,cs)) has been experimentally observed and theoretically explained. That is when S and N are brought together to form a weak link the Josephson effect can occur in this SN system even in the temperature range T(,cn) < T < T(,cs), when the N side is in the normal state. This Josephson effect is believed to happen between the S and a region of proximity-induced super- conductivity in N near the contact with S. We call this effect the proximity-induced Josephson effect. The temperature dependence of the Josephson critical current I(,c)(T) of the SN point contact junc- tions have been studied experimentally. The experiments have been performed on Ta/Mo, Ta/UBe(,13) and Nb/Ta point contacts etc. The theoretical model is based on the linearized Gor'kov equation (or linearized Ginzburg-Landau equation) combined with de Gennes boundary conditions. This model is applicable only in the vicinity of the T(,c) of the SN system. Thus, we studied I(,c)(T) of the SN junctions near their T(,c). Good agreement between experimental data and theoretical result is obtained;Along with the recent discovery of the superconductivity in heavy fermion materials CeCu(,2)Si(,2), UBe(,13) and UPt(,3) the old question of p-wave pairing superconductivity is raised again (in case of the exist- ence of strong spin-orbit scattering, it should be called odd parity superconductivity, since in that case the wave function of Cooper pairs cannot be separated into spin part and orbit part). These rare-earth and actinide compounds exhibit properties which cannot be explained by the conventional isotropic s-wave pairing supercon- ductivity (or BCS superconductivity) but are consistent with the varieties of p-wave (or odd parity) superconductivity. Among these three heavy fermion superconductors UBe(,13) is thought to be the best candidate for odd parity pairing for the reasons in Chapter 5 of this work. The proximity-induced Josephson effect is employed;to investigate the pairing state of UBe(,13). The results are found to favor an odd parity bulk superconducting ground state in UBe(,13); *DOE Report IS-T-1244. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy.