  We write down scalar field theory and gauge theory on two-dimensional
noncommutative spaces ${\cal M}$ with nonvanishing curvature and non-constant
non-commutativity. Usual dynamics results upon taking the limit of ${\cal M}$
going to i) a commutative manifold ${\cal M}_0$ having nonvanishing curvature
and ii) the noncommutative plane. Our procedure does not require introducing
singular algebraic maps or frame fields. Rather, we exploit the K\"ahler
structure in the limit i) and identify the symplectic two-form with the volume
two-form. As an example, we take ${\cal M}$ to be the stereographically
projected fuzzy sphere, and find magnetic monopole solutions to the
noncommutative Maxwell equations. Although the magnetic charges are conserved,
the classical theory does not require that they be quantized. The
noncommutative gauge field strength transforms in the usual manner, but the
same is not, in general, true for the associated potentials. We develop a
perturbation scheme to obtain the expression for gauge transformations about
limits i) and ii). We also obtain the lowest order Seiberg-Witten map to write
down corrections to the commutative field equations and show that solutions to
Maxwell theory on ${\cal M}_0$ are stable under inclusion of lowest order
noncommutative corrections. The results are applied to the example of
noncommutative AdS${}^2$.
