  We present a new class of well conditioned integral equations for the
solution of two and three dimensional scattering problems by homogeneous
penetrable scatterers. Our novel boundary integral equations result from
suitable representations of the fields inside and outside the scatterer as
combinations of single and double layer potentials acting on suitably defined
regularizing operators. The regularizing operators are constructed to be
suitable approximations of the admittance operators that map the transmission
boundary conditions to the exterior and respectively interior Cauchy data on
the interface between the media. The latter operators can be expressed in terms
of Dirichlet-to-Neumann operators. We refer to these regularized boundary
integral equations as Generalized Combined Source Integral Equations (GCSIE).
The ensuing GCSIE are shown to be integral equations of the second kind in the
case when the interface of material discontinuity is a smooth curve in two
dimensions and a smooth surface in three dimensions.
