My research employs topological analysis techniques to investigate the progression of Alzheimer’s disease (AD) using MRI data. I focus on the utilization of local persistence images (PIs) extracted from temporal lobe patches to classify AD and control subjects. My study evaluates model performance, analyzes topological heterogeneity within diagnostic categories and individual patients, examines the overlap between topological outliers and misclassified samples, and explores the distance of each image to median representations of AD and control subjects. Key findings include competitive classification results using local PIs, significant topological heterogeneity within diagnostic categories, and the identification of trends in patient clustering based on distance to median PIs. My study highlights the potential of topological analysis in understanding AD progression and suggests avenues for future research in disease subtyping and early detection.