  The scattering theory of the integrable statistical models can be generalized
to the case of systems with extended lines of defect. This is done by adding
the reflection and transmission amplitudes for the interactions with the line
of inhomegeneity to the scattering amplitudes in the bulk. The factorization
condition for the new amplitudes gives rise to a set of Reflection-Transmission
equations. The solutions of these equations in the case of diagonal $S$-matrix
in the bulk are only those with $S =\pm 1$. The choice $S=-1$ corresponds to
the Ising model. We compute the exact expressions of the transmission and
reflection amplitudes relative to the interaction of the Majorana fermion of
the Ising model with the defect. These amplitudes present a weak-strong duality
in the coupling constant, the self-dual points being the special values where
the defect line acts as a reflecting surface. We also discuss the bosonic case
$S=1$ which presents instability properties and resonance states. Multi-defect
systems which may give rise to a band structure are also considered. The exact
expressions of correlation functions is obtained in terms of Form Factors of
the bulk theory and matrix elements of the defect operator.
