  Extriangulated category was introduced by Nakaoka and Palu to give a
unification of properties in exact categories and triangulated categories. A
notion of tilting (or cotilting) subcategories in an extriangulated category is
defined in this paper. We give a Bazzoni characterization of tilting (or
cotilting) subcategories and obtain an Auslander-Reiten correspondence between
tilting (cotilting) subcategories and coresolving covariantly (resolving
contravariantly, resp.) finite subcatgories which are closed under direct
summands and satisfies some cogenerating (generating, resp.) conditons.
Applications of the results are given: we show that tilting (cotilting)
subcategories defined here unify many previous works about tilting theory in
module categories of Artin algebras and abelian categories admitting a
cotorsion triples; we also show that the results work for triangulated
categories with a proper class of triangles introduced by Beligiannis.
