This book provides an introduction to combinatorial commutative algebra
with particular emphasis on combinatorial techniques for multigraded
polynomial rings, semigroup algebras, and determined rings. The eighteen
chapters cover topics ranging from homological invariants of monomial
ideals and their polyhedral resolutions, to hands-on tools for studying
algebraic varieties with group actions, such as toric varieties, flag
varieties, quiver loci, and Hilbert schemes. Contains over 100 figures
and 250 exercises.