This cour is a lective cour for the graduate students and nior undergraduates in School of Mathematical Sciences. In this cour, the fundamental theories of the boundary problems of cond order linear and quasilinear elliptic partial differential equations will be systematically instructed. The contents consist of 1．L2 theory of cond order linear elliptic partial differential equations, 2．Schauder theory of econd order linear elliptic partial differential equations, 3．Lp theory of cond order linear elliptic partial differential equations, 4．Harnack inequality and H？lder estimates of solutions for elliptic equations of divergence form with bounded and measurable coefficients (De Giorgi-Nash estimates), 5．Existence of classical solutions for quasilinear elliptic partial differential equations, 6．Harnack inequality and H？lder estimates of solutions for elliptic equations of nondivergence form with bounded and measurable coefficients (Krylov-Safanov estimates). | 
