As an inorganic cousin of graphene, MoS2 monolayer has attracted considerable attention. However, a full understanding of its structure and stability is still lacking due to its dependence on experimental synthesis conditions. Using first-principle calculations combined with Boltzmann transport equation, we have extensively studied the geometry, energetics, electronic structure, optical absorption, and carrier mobility of various phases of MoS2. We have not only identified the stable phases of a MoS 2 monolayer, but also clarified the specific conditions under which different phases are formed. The possible pathways for transitions among different phases are also discussed.