Jordi Delgado - Department of Mathematics, University of the Basque Country, Faculty of Science and Technology, Barrio Sarriena, s/n ۴۸۹۴۰ Leioa, Spain
Enric Ventura - Departament de Matemàtiques, Universitat Politècnica de Catalunya and Institut de Matemàtiques de la UPC-BarcelonaTech, Barcelona, Catalunya

This survey is intended to be a fast (and reasonably updated) reference for the theory of Stallings automata and its applications to the study of subgroups of the free group, with the main accent on algorithmic aspects. Consequently, results concerning finitely generated subgroups have greater prominence in the paper. However, when possible, we try to state the results with more generality, including the usually overlooked non-(finitely-generated) case.

free group, subgroups, automaton, foldings, algorithmic problem