Spin dynamics in two dimensional quantum materials : a theoretical study : doctoral thesis accepted by Universitat Autònoma de Barcelona Spain This thesis focuses on the exploration of nontrivial spin dynamics in graphene based devices and topological materials using realistic theoretical models and state of the art quantum transport methodologies. The main outcomes of this work are: (i) the analysis of the crossover from diffusive to ballistic spin transport regimes in ultraclean graphene nonlocal devices and (ii) investigation of spin transport and spin dynamics phenomena (such as the (quantum) spin Hall effect) in novel topological materials such as monolayer Weyl semimetals WeTe2 and MoTe2. Indeed the ballistic spin transport results are key for further interpretation of ultraclean spintronic devices and will enable extracting precise values of spin diffusion lengths in diffusive transport and guide experiments in the (quasi)ballistic regime. Furthermore the thesis provides an in depth theoretical interpretation of puzzling huge measured efficiencies of the spin Hall effect in MoTe2 as well as a prediction of a novel canted quantum spin Hall effect in WTe2 with spins pointing in the yz plane. Introduction Fundamentals of Spin Dynamics in Two Dimensional Materials Quantum Transport Methodologies for Spin Transport Nonlocal Spin Dynamics in the Crossover from Diffusive to Ballistic Transport in Graphene Spin Dynamics in Low Symmetry Transition Metal Dichalcogenides.