Abstract: We rigorously justify the Prandtl equations and their higher-order boundary layer expansions from the Boltzmann equation in the hydrodynamic limit. Our setting considers Prandtl shear flows with small analytic perturbations. A central contribution is the derivation of precise estimates for the linearized Boltzmann equation with diffusive boundary conditions around a Prandtl layer. This resolves a key difficulty in connecting kinetic theory to boundary layer dynamics.