The γ-ray spectroscopy of Λ hypernuclei is one of the main subjects in strangeness nuclear physics program at the J-PARC Hadron Hall. By utilizing intense and pure K- beams available at J-PARC, hypernuclei will be produced via the (K-, π-) or (K-, π0) reactions and γ-rays will be detected in coincidence. The first experiment (E13) will be performed at the K1.8 beamline employing the SKS spectrometer with a modified setup (SksMinus) and a new Ge detector array Hyperball-J. It aims at the investigation of some of s, p and sd-shell hypernuclei (4ΛHe,7 ΛLi, 10ΛB, 11 ΛB, and 19ΛF) in order to measure the g-factor of Λ in a nucleus from a spin-flip B(M1) value and to examine various aspects of the hyperon-nucleon interactions (ΛN spin-dependent interactions, ΛN-ΣN coupling, charge symmetry breaking (CSB) in ΛN interaction, etc.). After E13, we will further investigate structures of a wide variety of Λ hypernuclei, such as p-shell, sd-shell, and medium and heavy hypernuclei up to 208 ΛPb, including neutron-rich ones, and also systematically measure B(E2) and B(M1) values for various hypernuclei to explore impurity effect to nuclear structure and nuclear medium effects to baryons, not only by the Doppler shift attenuation method (DSAM) but also by the γ-weak coincidence method.