This lecture covers the mechanics of elastic deformation, focusing on topics such as elastic rigidity, young modulus, internal energy, stiffness, and temperature dependence. It discusses the behavior of materials under low deformations, the influence of temperature on elasticity, and the stiffness coefficients for various materials. The lecture also delves into the isotropy of materials, thermal expansion, and the generalized Hooke's law. Additionally, it explores elasticity in heterogeneous materials, including polycrystals and multi-phase materials, and the challenges posed by their heterogeneity.