1 introduction 2 A Theorem of J. Hadamard 3 Asymptotic and Sequential Asymptotic Values of Polynomial Maps 4 The Asymptotic Values of a Polynomial Map C2 �� C2 Form a Va-riety which is the Union of Two Natural Algebraic Curves in C2 5 The Resultant Formulation of the Jacobian Conjecture 6 The Jacobian Conjecture in Dimension 2 is Decidable 7 A Straight Forward Inductive Approach Fails 8 Grading an Algebra with a Derivation - Introduction 9 Grading an Algebra According To a Derivation 10 The Structure of the D-classes 11 Application to Automorphisms of Polynomial Rings 12 Elementary Properties of Resultants of Jacobian Pairs 13 Invertible Morphisms their Resultants and Inversion Formulas 14 The Rigidity of Morphisms 15 The Fibre Theorem 16 Expressing the Jacobian and the Resultant in Grassmann Coordi-nates 17 One More Inversion Formula and an Equivalent Formulation to the Jacobian Conjecture 18 Parametrization of the Jacobian Variety 19 More Statements which are Equivalent to the Jacobian Conjecture Bibliography ��݋��ӛ