  Adopting the pullback formalism, a new linear connection in Finsler geometry
has been introduced and investigated. Such connection unifies all formerly
known Finsler connections and some other connections not introduced so far.
Also, our connection is a Finslerian version of the Tripathi connection
introduced in Riemannian geometry. The existence and uniqueness of such
connection is proved intrinsically. An explicit intrinsic expression relating
this connection to Cartan connection is obtained. Some generalized Finsler
connections are constructed from Tripathi Finsler connection, by applying the
P1-process and C-process introduced by Matsumoto. Finally, under certain
conditions, many special Finsler connections are given.
