Intro -- Contents -- Preface -- Speakers of the INdAM School -- One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations -- Maximum Principles and symmetry results in sub-Riemannian settings -- Symétrie: si, mais seulement si? -- Minimal surfaces and minimizers of the Ginzburg-Landau energy -- Green's Function Estimates for Some Linear and Nonlinear Elliptic Problems -- Monotonicity of the solutions of quasilinear elliptic equations in the half-plane with a changing sign nonlinearity -- Some inequalities associated with semilinear elliptic equations with variable coefficients and applications -- A Liouville theorem for non local elliptic equations -- On a conjecture by De Giorgi in dimensions 9 and higher.