The Enumerative Theory of Conics after Halphen Conics Complete conics Systems of conics Equations of the degeneration hypersurfaces Conditions imposed on conics Action of the projective group and proper solutions of an enumarative problem Genericity of the data of conditions Local characters of a condition Halphens first formula Computation of characteristic numbers Examples Strict equivalence of conditions Systems of conics contained in Sp q Conics satisfying five independent conditions Cycles on W and on B Multiplicity cycles and Noethers formula Improper intersection numbers Generalization of Halphens formula to conditions of higher order Examples of higher order conditions Strict equivalence of conditions Enumerative ring of W Computation of products in hal· (W) Further examples.