This lecture covers the Eshelby method for ellipsoidal inclusions, focusing on mechanics of particles undergoing shape changes due to eigenstrains. It explains the stress and strain fields, elastic energy, and modulus mismatch effects. The instructor discusses the analytical solution for ellipsoidal particles and the Eshelby tensor. The lecture also delves into Voigt notation for the Eshelby tensor and the Fourth Order Identity tensor. It concludes with a detailed explanation of the displacement field, strain fields, and the mechanics problem solution using red point forces.