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This lecture covers the principles of hydrogen evolution catalysis, focusing on the overpotential in the Fe-porphyrin system, thermodynamic potentials of HER, and global analysis of catalytic systems. It also discusses the general mechanism for HER catalyzed by molecular complexes, overpotential calculations, and the biomimetic approach. The lecture delves into the proposed catalytic cycle for HER by [FeFe]-hydrogenase, bioinspired nickel complexes, and the role of nitrogen in proton acceptance. Various molecular catalysts for HER are explored, along with their mechanisms and potential applications. The lecture concludes with remarks on the development of non-precious catalysts for large-scale hydrogen evolution.