  Let M be an irreducible Riemannian symmetric space. The index i(M) of M is
the minimal codimension of a totally geodesic submanifold of M. In previous
work the authors proved that i(M) is bounded from below by the rank rk(M) of M.
In this paper we classify all irreducible Riemannian symmetric spaces M for
which the equality holds, that is, rk(M) = i(M). In this context we also obtain
an explicit classification of all non-semisimple maximal totally geodesic
submanifolds in irreducible Riemannian symmetric spaces of noncompact type and
show that they are closely related to irreducible symmetric R-spaces. We also
determine the index of some symmetric spaces and classify the irreducible
Riemannian symmetric spaces of noncompact type with i(M) = 4,5 or 6.
