Understanding properties of quasiparticles in novel two-dimensional (2D) semiconductors, such as atomically thin transition metal dichalcogenides (TMDCs) and group-III metal monochalcogenides, is among the most interesting topics in condensed matter physics in recent years. Their distinctive excitonic effects resulting from strong Coulomb interaction in the truly 2D limit, strong light-matter interaction, spin-valley locking (in TMDCs), and the availability of new degrees of freedom (stacking and twisting) for tuning electronic properties make these materials a unique platform for exploring excitonic physics and for potential optoelectronic applications. In this thesis, we use low temperature optical magneto-spectroscopy to probe the fundamental properties of excitons and excitonic complexes in monolayer TMDCs and few-layer InSe. In the first part of this thesis, we identified and characterized the intrinsic spin conserved (bright) and spin-flip forbidden (dark) exciton states as well as their related exciton complexes in monolayer WSe2 and MoSe2. The dark excitons are originated from the spin-orbital coupling splitting of the conduction band. We demonstrate that by applying strong in-plane magnetic fields, one can induce mixing and splitting of bright and dark exciton branches, which enables an accurate spectroscopic determination of their energies. We establish, for the first time, the bright-dark excitons splitting in an archetypal TMDC monolayer semiconductor, MoSe2, which helped to resolve a long-standing puzzle of its surprisingly high valley depolarization. In the second part of the thesis, we examine the optical properties of monolayer MoSe2 away from the charge neutrality point. Monolayer TMDCs have extremely high exciton binding energies, which makes the excitonic effects dominate the optical processes even at high electron densities when the Fermi level is in the conduction band. Here, we study excitons dressed by the Fermi sea of electrons forming new quasi-particles, repulsive and attractive exciton-polarons, as well as their Landau quantization at high magnetic fields. In the third part of the thesis, we study another 2D direct-gap semiconductor, InSe, in the regime where the Fermi energy approaches the exciton binding energy. Due to the high mobility of electrons in the conduction and the flat valence band, few-layer InSe provides a nearly ideal system to study many-body phenomena using optical spectroscopy. In this thesis, we report the observation of Fermi edge singularity, spectroscopic measurements of quantum Hall gaps, and detection of possible signatures of fractional quantum Hall states in InSe.
