  The total surgery obstruction of a finite n-dimensional Poincare complex X is
an element s(X) of a certain abelian group S_n (X) with the property that for n
>= 5 we have s(X) = 0 if and only if X is homotopy equivalent to a closed
n-dimensional topological manifold. The definitions of S_n (X) and s(X) and the
property are due to Ranicki in a combination of results of two books and
several papers. In this paper we present these definitions and a detailed proof
of the main result so that they are in one place and we also add some of the
details not explicitly written down in the original sources.
