Описание:Introduction to the moduli space theory and to dessin d'enfant theory are provided. Interrelations between these subjects are discussed, including several moduli space compactifications. The course was delivered at the University of Lisboa, Faculty of Science, Centro de Estruturas Lineares e Combinatórias, http://celc.ciencias.ulisboa.pt/meetings/guterman-kreinesMay2012.html in May-June 2012.