In this proposal we will model time-dependent spectroscopy in ultra-thin two-dimensional materials, with the goal of simulating ultra-fast optical phenomena. We will use a fully first-principles theoretical approach which will give predictive character to our simulations and will allow us to investigate how the environment (defects and substrates) tunes the optical properties. We will apply our theory to semiconducting monolayer transition dichalcogenides (TMDs), such as MoS2, MoSe2, WS2 and WSe2.Research in ultra-thin two-dimensional (2D) materials has been booming since the discovery of graphene along with its interesting physical properties. Semiconducting TMDs form a distinct and remarkable group of 2D-materials and they have emerged as graphene alternative in applications where a bandgap is needed. They have direct bandgaps, ranging from 1.5 to 2.3 eV, a high carrier mobility, and mechanical flexibility, which make them suitable for transistors with high current on/off ratios, and also for optoelectronic devices for light harvesting and generation. Another striking feature of TMDs is the presence of two inequivalent minima (valleys) in the conduction band which can be selectively excited by circularly left or right polarized light. Due to the symmetry of the system and strong spin-orbit coupling, the ?valley? degree of freedom is a good quantum number that can serve as an information carrier. This gives rise to the potential new field of ?valleytronics?, an analogoy to spintronics. Good performance of TMDs in optoelectronics and valleytronics depends critically on the efficient light absorption and subsequently excited carrier relaxation dynamics. While light absorption is well described using time-independent methods, reliable modelling of the relaxation dynamics of 2D-materials is in its infancy. On the experimental side we find many interesting results. Pump-probe ultra-fast spectroscopy investigations show complex dynamics, highly influenced by the presence of defects and underlying substrate. To the typical relaxation channels of intrinsic TMDs (electron-electron and electron-phonon scatterings) we have to add defect-assisted exciton decay and the modulation of the electronic structure by the substrate. Thus, measured lifetimes of photo-generated carriers exhibit a strong dependence on the environment. Concerning the Valley Hall effect, interplay between intra-valley and inter-valley scatterings will dictate the valley polarization dynamics, and hence the applicability of TMDs in valleytronics. Such interplay is also affected by defects and substrates. The ongoing experimental research in ultra-fast optics of 2D-materials demands realistic modelling for a better understanding of the physics of relaxation pathways. We propose a novel approach, implementing first-principles methods for the study of ultra-fast spectroscopy in 2D-materials.The goal of our project is to quantitatively determine the relaxation channels of monolayer TMDs, within a fully first-principles approach. We will use many-body perturbation theory on top of density-functional theory to describe time-dependent spectroscopy, obtaining time-dependent photo-luminescence and transient absorption spectra. We will identify which relaxation channels dominate the photo-generated carrier dynamics, and the influence of defects and substrates in such dynamics. Simulation of carrier dynamics and understanding of ultra-fast optics of TMDs is crucial for the design of a new generation of TMDs-devices based on the Valley Hall effect and to explore the use of semiconducing TMDs for more efficient solar cells.