  In this paper, we establish the general theory of (2+1)-dimensional
topological quantum field theory (in short, TQFT) with a Verlinde basis. It is
a consequence that we have a Dehn surgery formula for 3-manifold invariants for
this kind of TQFT's. We will show that Turaev-Viro-Ocneanu unitary TQFT's
obtained from subfactors satisfy the axioms of TQFT's with Verlinde bases.
Hence, in a Turaev-Viro-Ocneanu TQFT, we have a Dehn surgery formula for
3-manifolds. It turns out that this Dehn surgery formula is nothing but the
formula of the Reshetikhin-Turaev invariant constructed from a tube system,
which is a modular category corresponding to the quantum double construction of
a C^*-tensor category. In the forthcoming paper, we will exbit computations of
Turaev-Viro-Ocneanu invariants for several ``basic 3-manifolds ''. In Appendix,
we discuss the relationship between the system of M_{infinity}-M_{infinity}
bimodules arising from the asymptotic inclusion M V M^{op} subset M_{infinity}
constructed from N subset M and the tube system obtained from a subfactor N
subset M.
