This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jurgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Alvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Grobner basis theory allows us...