Richard Schoen of Stanford University lectures on stability theory for minimal submanifolds, delivered at the Institute for Advanced Study as part of a workshop honoring Jim Simons. Schoen works through the variational framework that defines minimal submanifolds as critical points of the area functional, then turns to the second variation and the stability operator that determines whether a given minimal submanifold is a local minimum of area or merely a saddle point. He discusses the role of the Jacobi operator, index theory, and curvature conditions that control stability, connecting the analysis to broader questions in geometric analysis that Simons himself helped shape through his work on minimal varieties and the Simons cone. The talk assumes familiarity with Riemannian geometry and differential equations, building from classical examples toward current open problems in the field. Recorded in Simonyi Hall at IAS, it runs just over an hour and is aimed at researchers and graduate students in geometric analysis.