This lecture covers the basics of the Finite Element Method (FEM) and its applications in solving Partial Differential Equations (PDEs). It explains the discretization process, matrix solving, and time integration. The instructor demonstrates the FEM through an example, showing the transition from the strong form to the weak form and the assembly of the stiffness matrix. The lecture also introduces the use of Comsol Multiphysics for multiphysics simulations, emphasizing the importance of stable and accurate numerical methods for PDEs.