Functions with positive real part -- Special classes: convex, starlike, real, typically real, close-to-convex, bounded boundary rotation -- The Pólya-Schoenberg conjecture -- Representation of continuous linear functionals -- Faber polynomials -- Extremal length and equicontinuity -- Compact families ?(D,?1,?2,P,Q) of univalent functions normalized by two linear functionals -- Properties of extreme points for some compact families ?(D,?1,?2,P,Q) -- Elementary variational methods -- Application of Schiffer’s boundary variation to linear problems -- Application to some nonlinear problems -- Some properties of quasiconformal mappings -- A variational method for q.c. mappings -- Application to families of conformal and q.c. mappings -- Sufficient conditions for q.c. extensions.