Based on rst principles calculations the structural, mechanical stability and electronic properties of molybdenum chalcogenides 2H-MoX2 (X = S, Se, Te) have been studied using density functional theory (DFT). The generalized gradient approximation (GGA) proposed by Perdew, Burke and Ernzerhof (PBE) was employed together with the projector augmented plane wave (PAW) method. The van der Waals interactions in the Grimme (DFT-D2) and Lundqvist and Langreth (vdW-DF) approximations have been added on top of PBE or revised PBE in order to take into account the weak interactions between layers of 2H-MoX2 (X = S, Se, Te). The structural properties include the equilibrium lattice parameters, the cohesive energy and the formation energy. Besides we have studied the mechanical stability of these compounds by examining the elastic constants using the PBE, vdW-DF, and DFT-D2 approximations. Other quantities related to the mechanical properties such as the Young's modulus, the Poisson's ratio and the bulk modulus were also calculated. Electronic properties of bulk 2H-MoX2 (X = S, Se, Te) have been investigated using density functional theory (via band structure and projected density of state), and a partially self-consistent GW (GW0) approximation. We have investigated electronic properties ( band structure) for monolayers 1H-MoX2 (X = S, Se, Te) using a single shot GW (G0W0) approximation. Optical properties for monolayer 1H-MoX2 (X = S, Se, Te) were studied using the Bethe-Salpeter equation (BSE).