  This two-parts paper offers a survey of linear logic and ludics, which were
introduced by Girard in 1986 and 2001, respectively. Both theories revisit
mathematical logic from first principles, with inspiration from and
applications to computer science. The present part I covers an introduction to
the connectives and proof rules of linear logic, to its decidability
properties, and to its models. Part II will deal with proof nets, a graph-like
representation of proofs which is one of the major innovations of linear logic,
and will present an introduction to ludics.
