  In the random geometric graph $G(n,r_n)$, $n$ vertices are placed randomly in
Euclidean $d$-space and edges are added between any pair of vertices distant at
most $r_n$ from each other. We establish strong laws of large numbers (LLNs)
for a large class of graph parameters, evaluated for $G(n,r_n)$ in the
thermodynamic limit with $nr_n^d =$ const., and also in the dense limit with $n
r_n^d \to \infty$, $r_n \to 0$. Examples include domination number,
independence number, clique-covering number, eternal domination number and
triangle packing number. The general theory is based on certain subadditivity
and superadditivity properties, and also yields LLNs for other functionals such
as the minimum weight for the travelling salesman, spanning tree, matching,
bipartite matching and bipartite travelling salesman problems, for a general
class of weight functions with at most polynomial growth of order
$d-\varepsilon$, under thermodynamic scaling of the distance parameter.
