This paper presents quasiparticle self-consistent GW (QSGW) calculations of the band structures and effective mass parameters for bulk, monolayer, and bilayer MoS₂. The results show that monolayer MoS₂ transitions from an indirect to a direct band gap, while bulk and bilayer MoS₂ remain indirect. The calculated direct gap in monolayer MoS₂ is 0.2 eV larger than the QSGW result, and the calculated transitions in monolayer and bilayer are overestimated by more than 0.5 eV compared to optical absorption measurements. This overestimation is attributed to the strong excitonic effects in two-dimensional systems. The A and B exciton peaks in monolayer and bilayer MoS₂ are explained by the splitting of the valence band, which in monolayer arises purely from spin-orbit coupling, while in bilayer is a combination of interlayer and spin-orbit coupling effects. The exciton binding energies are large in monolayer and bilayer due to the strongly reduced dielectric constants. The calculated effective Bohr radii are 9.3 Å for monolayer and 13.0 Å for bilayer, leading to ground state binding energies of 0.897 eV and 0.424 eV, respectively. These results agree well with experimental data for the A and B excitons and the indirect exciton in bilayer MoS₂. The study also discusses the applicability of the Wannier exciton theory for monolayer and bilayer MoS₂, noting that it is not applicable to the Σ_min exciton due to its larger reduced mass and unusual anisotropic mass. The results show that the transition from indirect to direct gap between bulk and monolayer actually occurs between bilayer and monolayer, in agreement with experimental findings. The calculations are supported by various references and methods, including the use of the FP-LMTO method within the local density approximation and the QSGW method. The work was supported by the National Science Foundation.This paper presents quasiparticle self-consistent GW (QSGW) calculations of the band structures and effective mass parameters for bulk, monolayer, and bilayer MoS₂. The results show that monolayer MoS₂ transitions from an indirect to a direct band gap, while bulk and bilayer MoS₂ remain indirect. The calculated direct gap in monolayer MoS₂ is 0.2 eV larger than the QSGW result, and the calculated transitions in monolayer and bilayer are overestimated by more than 0.5 eV compared to optical absorption measurements. This overestimation is attributed to the strong excitonic effects in two-dimensional systems. The A and B exciton peaks in monolayer and bilayer MoS₂ are explained by the splitting of the valence band, which in monolayer arises purely from spin-orbit coupling, while in bilayer is a combination of interlayer and spin-orbit coupling effects. The exciton binding energies are large in monolayer and bilayer due to the strongly reduced dielectric constants. The calculated effective Bohr radii are 9.3 Å for monolayer and 13.0 Å for bilayer, leading to ground state binding energies of 0.897 eV and 0.424 eV, respectively. These results agree well with experimental data for the A and B excitons and the indirect exciton in bilayer MoS₂. The study also discusses the applicability of the Wannier exciton theory for monolayer and bilayer MoS₂, noting that it is not applicable to the Σ_min exciton due to its larger reduced mass and unusual anisotropic mass. The results show that the transition from indirect to direct gap between bulk and monolayer actually occurs between bilayer and monolayer, in agreement with experimental findings. The calculations are supported by various references and methods, including the use of the FP-LMTO method within the local density approximation and the QSGW method. The work was supported by the National Science Foundation.