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Summary: Background: Primary open-angle glaucoma (POAG) is an optic neuropathy characterized by progressive degeneration of the optic nerve that leads to irreversible visual impairment. Multiple epidemiological studies suggest an association between POAG and major neurodegenerative disorders (Alzheimer's disease, amyotrophic lateral sclerosis, frontotemporal dementia, and Parkinson's disease). However, the nature of the overlap between neurodegenerative disorders, brain morphology and glaucoma remains inconclusive. Method: In this study, we performed a comprehensive assessment of the genetic and causal relationship between POAG and neurodegenerative disorders, leveraging genome-wide association data from studies of magnetic resonance imaging of the brain, POAG, and four major neurodegenerative disorders. Findings: This study found a genetic overlap and causal relationship between POAG and its related phenotypes (i.e., intraocular pressure and optic nerve morphology traits) and brain morphology in 19 regions. We also identified 11 loci with a significant local genetic correlation and a high probability of sharing the same causal variant between neurodegenerative disorders and POAG or its related phenotypes. Of interest, a region on chromosome 17 corresponding to MAPT, a well-known risk locus for Alzheimer's and Parkinson's disease, was shared between POAG, optic nerve degeneration traits, and Alzheimer's and Parkinson's diseases. Despite these local genetic overlaps, we did not identify strong evidence of a causal association between these neurodegenerative disorders and glaucoma. Interpretation: Our findings indicate a distinctive and likely independent neurodegenerative process for POAG involving several brain regions although several POAG or optic nerve degeneration risk loci are shared with neurodegenerative disorders, consistent with a pleiotropic effect rather than a causal relationship between these traits. Funding: PG was supported by an NHMRC Investigator Grant (#1173390), SM by an NHMRC Senior Research Fellowship and an NHMRC Program Grant (APP1150144), DM by an NHMRC Fellowship, LP is funded by the NEI EY015473 and EY032559 grants, SS is supported by an NIH-Oxford Cambridge Fellowship and NIH T32 grant (GM136577), APK is supported by a UK Research and Innovation Future Leaders Fellowship, an Alcon Research Institute Young Investigator Award and a Lister Institute for Preventive Medicine Award.