We present an overview of the approximation theory in
 combinatorial optimization. As an application we consider the 
 Generalized Minimum Spanning Tree (GMST) problem which is defined on an undirected complete graph with the nodes partitioned into
 clusters and non-negative costs are associated to the edges. This
 problem is NP-hard and it is known that a
 polynomial approximation algorithm cannot exist. We present an
 in-approximability result for the GMST problem and under special
 assumptions: cost function satisfying the triangle inequality and
 with cluster sizes bounded by \(\rho\), we give an approximation
 algorithm with ratio \(2 \rho\).