chapter 1 A theorem of Eakin and Sathaye and Green’s hyperplane restriction theorem / chapter 2 Liaison of varieties of small dimension and deficiency modules / chapter 3 Regularity jumps for powers of ideals / chapter 4 Integral closure of ideals and annihilators of homology / chapter 5 Poincare´ series of surface singularities / chapter 6 Multi-graded Hilbert coefficients / chapter 7 Torsion freeness and normality of blowup rings of monomial ideals / chapter 8 Monomial ideals via square-free monomial ideals / chapter 9 When does the equality I2 QI hold true in Buchsbaum rings? / chapter 10 Integral closures of ideals in completions of regular local domains / chapter 11 The components of a variety of matrices with square zero and submaximal rank / chapter 12 The support of top graded local cohomology modules / chapter 13 An approach to the uniform Artin-Rees theorems from the notion of relation type / chapter 14 Castelnuovo-Mumford regularity and finiteness of Hilbert functions / chapter 15 Differential idealizers and algebraic free divisors / chapter 16 Gorenstein rings call the tune / chapter 17 On free integral extensions generated by one element / chapter 18 Degeneration and G-dimension of modules