  In this thesis we are interested in studying algebraic properties of monomial
algebras, that can be linked to combinatorial structures, such as graphs and
clutters, and to optimization problems. A goal here is to establish bridges
between commutative algebra, combinatorics and optimization. We study the
normality and the Gorenstein property-as well as the canonical module and the
a-invariant-of Rees algebras and subrings arising from linear optimization
problems. In particular, we study algebraic properties of edge ideals and
algebras associated to uniform clutters with the max-flow min-cut property or
the packing property. We also study algebraic properties of symbolic Rees
algebras of edge ideals of graphs, edge ideals of clique clutters of
comparability graphs, and Stanley-Reisner rings.
