  We present a general analysis of all the possible soft breakings of N=2
supersymmetric QCD, preserving the analytic properties of the Seiberg-Witten
solutions for the SU(2) group with Nf=1, 2, 3 hypermultiplets. We obtain all
the couplings of the spurion fields in terms of properties of the
Seiberg-Witten periods, which we express in terms of elementary elliptic
functions by uniformizing the elliptic curves associated to each number of
flavors. We analyze in detail the monodromy properties of the softly broken
theory, and obtain them by a particular embedding into a pure gauge theory with
higher rank group. This allows to write explicit expressions of the effective
potential, which are close to the exact answer for moderate values of the
supersymmetry breaking parameters. The vacuum structures and phases of the
broken theories will be analyzed in the forthcoming second part of this paper.
