  This article is the first of a pair of articles dealing with the Iwasawa
theory of modular forms of weight 1 and, more generally, of Artin
representations satisfying certain conditions. The main results in this part
analyze the structure of certain Selmer groups for the Artin representation. In
particular, it is shown that the Selmer groups are co-torsion as
$\Lambda$-modules. For each Selmer group, we consider a generator of the
characteristic ideal of its Pontrjagin dual. We call that the algebraic p-adic
L-function. We also construct an analytic $p$-adic L-function via deformation
to higher weights. Both of these $p$-adic L-functions should conjecturally have
an interpolation property involving $p$-adic logarithms of global units
analogous to Stark units. The proof of the interpolation property for the
algebraic $p$-adic L-function will be given in Part 2 of this work.
