Study of nuclear weak processes, especially the Gamow-Teller (GT) transitions, starting from stable as well as unstable nuclei, is one of the key issues in nuclear physics and nuclear astrophysics. In the collapsing core of pre-supernova stars, where the temperature of a few ×10 9 K is expected, electron capture and neutrino induced reactions play important roles. In these reactions, GT transition is one of the main actors. However, due to the weakness of the weak interaction causing these reactions, experimental study of these reactions that can happen under such extreme stellar conditions are difficult. Direct information on GT transitions and the GT transition strength B(GT) by using the weak interaction itself has been available only from β -decay measurements. However, B(GT) values are usually derived only for low-lying states. Note that the study of the feedings to higher excited states is difficult in a β -decay study, because the phase-space factor ( f -factor) decreases with the excitation energy. The GT transitions are caused by the σ τ-type operator. It is known that the nuclear excitation by means of the σ τ-type nuclear strong interaction becomes dominant in charge-exchange (CE) reactions performed at small scattering angles and intermediate incident energies. Therefore, we study the GT transitions using hadronic ( 3 He,t), CE reactions. By realizing dispersion matching conditions, high energy-resolution has been realized and detailed GT strength distributions can be studied up to high excitation energies. Under the assumption that isospin is a good quantum number, symmetry is expected for the structure of mirror nuclei and the GT transitions starting from them. The results from ( 3 He,t) reactions on stable p f -shell nuclei are compared and also combined with the complementary β -decay studies for the mirror proton-rich nuclei in the region far-from-stability. Since the pass of the rp-process nucleosynthesis goes thorough these proton-rich nuclei, the information on GT transitions from them are essential for the better understanding of the process.