Intro -- Contents -- Preface -- On the classification of toric singularities -- An overview on the minimal free resolutions of lexsegment ideals -- Cohen-Macaulay squarefree lexsegment ideals generated in degree 2 -- On simple A-multigraded minimal resolutions -- Tangent cones of numerical semigroup rings -- The Igusa local zeta functions of GL2(Qp)-orbit of Fermat's binary form -- Arithmetical rank of monomial ideals of deviation two -- A survey of combinatorial aspects in the topology of complex hyperplane arrangements -- A class of locally complete intersection multiple structures on smooth algebraic varieties as support -- Topological Cohen-Macaulay criteria for monomial ideals -- Regularity and the case of few generators for Stanley-Reisner ideals of subword complexes -- The type of the base ring associated to a transversal polymatroid.