Volume I: Quadratic cremona transformations Analysis of singularities of plane algebraic curves Linear systems of plane curves Planar cremona transformations Multiple correspondences between two planes Involutions on rational curves Correspondences on non-rational curves Cremona transformations in space and hyperspace $(1, 2)$ correspondences between $S^{\prime}_r$ and $S_r, r> 2$ Reduction of singularities of space curves and surfaces Multiple correspondence in space and hyperspace The mapping of a rational surface on a plane The mapping of a rational congruence on a plane Involutions on irrational surfaces Transcendental theory Singular correspondences between algebraic curves Hyperelliptic surfaces and abelian varieties Volume II: Curves and ruled surfaces The mapping of systems of curves Systems of lines in $S_n$; Irregular surfaces Cremona transformations Multiple correspondences Surfaces and varieties.