¿Well posed¿ boundary value problems.- Existence principle.- The function spaces and Hm.- The trace operator. Sobolev and Ehrling lemmas.- Elliptic linear systems. Interior regularity.- Existence of local solutions for elliptic systems.- Semiweak solutions of BVP for elliptic systems.- Regularity at the boundary: preliminary lemmas.- Regularity at the boundary: tangential derivatives.- Regularity at the boundary: final results.- The classical elliptic BVP of Mathematical physics: 2nd order linear PDE..- The classical elliptic BVP of Mathematical Physics: Linear Elastostatics.- The classical elliptic BVP of Mathematical Physics: Equilibrium of thin plates.- Strongly elliptic operators. G¿rding inequality. Eigenvalue problems.- Eigenvalue problems. The Rayleigh-Ritz method.- The Weinstein¿Aronszajn method.- Construction of the intermediate