Mini-course of numerical semigroups held at CMUP, Universidade do Porto.
The course was divided into three lessons.
Special thanks CMUP and the Departamento de Matemática Pura for their kind hospitality, and in particular to Manuel Delgado with whom I enjoyed working, running and programming in numerical semigroups.
It is difficult to collect a complete list of references related to numerical semigroups. At the time this course was given, our friend Jorge Ramírez Alfonsín already did wonderful work in his book. Barucci, Dobbs and Fontana wrote a marvelous monograph highlighting the connections between numerical semigroups and analytically unramified one-dimensional local domains, which in addition can be used as a dictionary for the names we use for the invariants of a numerical semigroup. Barucci recently wrote a nice survey on numerical semigroup rings that will be included in a book in honor of Gilmer (to whom all the people working in commutative semigroups are in debt). Of course, I must mention Rosales’ production in the field of numerical semigroups, since he was who introduced me to this fascinating world. And indeed I am happy he did...