Plates and shells are common structural elements in many engineering applications and have recently become very important for applications to blades in high speed turbomachines. Basic theories concerning plates, variational principles and the use of delta operator that facilitate the derivation of differential equations and boundary conditions are explained in a lucid manner. Lagrange, Ritz and Galerkin energy methods, Levy and Kantorovich principles, classical solutions of Navier and Nadai and different finite elements are given in detail. The static as well as dynamic behavior principles are presented.