  We discuss a study of domain walls in $N=1, d=4$ supergravity. The walls
saturate the Bogomol'nyi bound of wall energy per unit area thus proving
stability of the classical solution. They interpolate between two vacua whose
cosmological constant is non-positive and in general different. The matter
configuration and induced geometry are static. We discuss the field theoretic
realization of these walls and classify three canonical configurations with
examples. The space-time induced by a wall interpolating between the Minkowski
(topology $\Re^{4}$) and anti-de~Sitter (topology $S^{1}(time) \times
\Re^{3}(space)$) vacua is discussed. (Comments in chapter 6 on AdS-Minkowski
wall induced space-time have been slightly changed)
