Dissertação de Doutoramento em Matemática (Álgebra, Lógica e Fundamentos), Faculdade de Ciências, Universidade de Lisboa, Portugal, 2006

In this dissertation we considered some monoids of transformations on a finite chain, namely of order-preserving or order-reversing transformations and, similarly, of orientation-preserving or orientation-reversing transformations. For these monoids, we
calculated generators and the rank, described Green relations and the maximal subgroups, determined the cardinality and the number of idempotents and, finally, we described the congruences and exhibited
presentations.