  This is the first of a sequence of papers proving the quantum invariance
under ordinary flops over an arbitrary smooth base.
  In this first part, we determine the defect of the cup product under the
canonical correspondence and show that it is corrected by the small quantum
product attached to the extremal ray. We then perform various reductions to
reduce the problem to the local models.
  In Part II, we develop a quantum Leray--Hirsch theorem and use it to show
that the big quantum cohomology ring is invariant under analytic continuations
in the K\"ahler moduli space for ordinary flops of splitting type. In Part III,
together with F. Qu, we remove the splitting condition by developing a quantum
splitting principle, and hence solve the problem completely.
