BACKGROUNDAlzheimer's disease (AD) might impact the complexity of cerebral cortex, and the underlying biological mechanisms responsible for cortical changes in the AD cortex remain unclear.METHODSFifty-eight participants with AD and 67 normal controls underwent high-resolution 3 T structural brain MRI. Using surface-based morphometry (SBM), we created vertex-wise maps for group comparisons in terms of five measures: cortical thickness, fractal dimension, gyrification index, Toro's gyrification index and sulcal depth respectively. Five machine learning (ML) models combining SBM parameters were established to predict AD. In addition, transcription-neuroimaging association analyses, as well as Mendelian randomization of AD and cortical thickness data, were conducted to investigate the genetic mechanisms and biological functions of AD.RESULTSAD patients exhibited topological changes in cortical complexity, with increased complexity in the frontal and temporal cortex and decreased complexity in the insula cortex, alongside extensive cortical atrophy. Combining different SBM measures could aid disease diagnosis. The genes involved in cell structure support and the immune response were the strongest contributors to cortical anatomical features in AD patients. The identified genes associated with AD cortical morphology were overexpressed or underexpressed in excitatory neurons, oligodendrocytes, and astrocytes.CONCLUSIONComplexity alterations of the cerebral surface may be associated with a range of biological processes and molecular mechanisms, including immune responses. The present findings may contribute to a more comprehensive understanding of brain morphological patterns in AD patients.