A new general formalism for a linear kinetic theory is proposed. It is based on a diagrammatic analysis of the linear integral operators containing equilibrium correlations. The diagrams are similar to the Mayer graphs but possess two kinds of root-points. This new diagrammatic technique is used to analyse the BBGKY hierarchy for a hard-sphere fluid. As a result a new hierarchy of evolution equations is obtained in which the Enskog-like renormalization of the binary collisions has been explicitly carried out, thus the previous ideas of Resibois and Lebowitz have been fully implemented. The final results are shown to be equivalent to those of van Beijeren. Possible further applications of the proposed formalism are indicated and will be the subject of following publications.
