Transport phenomena give structure to flames, thus, being a key mechanism of combustion reactions. Molecular hydrogen (H2) combustion is characterized by strong preferential diffusion effects due to differences between the diffusion coefficients of each species involved in the reaction. Moreover, in specific areas of the flame, counter-Fickian diffusive motions, characterized by the displacement of species from low concentration areas to high concentration areas, are observed. This leads to the creation of zones within the flame where the combustion is enhanced and other where combustion is deteriorated, implying the rise of non-uniformities. To analyze preferential diffusion effects, the thesis first details the fundamental notions of combustion by reminding the governing equations and characteristics of premixed flames. A detailed chemistry study is then performed based on the Maxwell-Stephan diffusion equations. It aims to precisely analyze an H2-air one dimensional flame using multiple transport models as the Lewis unity, mixture average and the multicomponent transport models. Thus, the evolution of the combustion reaction’s parameters such as the mass and mixture fractions, temperature and heat release rate are examined. The effects of the equivalence ratio are also considered, enabling to evaluate lean, stoichiometric and rich combustion. Moreover, a budget analysis of the species equation terms is performed to determine the evolution and importance of the convection, diffusion, and chemical source terms in the transport process. To account for multidimensional effects a premixed H2-air slit burner flame is numerically simulated, and the Flamelet Generated Manifold (FGM) method is introduced in the last part. The numerical simulations are performed on the Mare Nostrum 4 supercomputer from the Barcelona Supercomputing Center (BSC-CNS) which enables both thermodynamic and thermokinetic properties of the flame to be analyzed.