  Maximal abelian subalgebras of one of the classical real inhomogeneous Lie
algebras are constructed, namely those of the pseudoeuclidean Lie algebra
e(p,q). Use is made of the semidirect sum structure of e(p,q) with the
translations T(p+q) as an abelian ideal. We first construct splitting MASAs
that are themselves direct sums of abelian subalgebras of o(p,q) and of
subalgebras of T(p+q). The splitting subalgebras are used to construct the
complementary nonsplitting ones. We present general decomposition theorems and
construct indecomposable MASAs for all algebras e(p,q), p \geq q \geq 0. The
case of q=0 and 1 were treated earlier in a physical context. The case q=2 is
analyzed here in detail as an illustration of the general results.
