Aut\`omats de Stallings, un cam\'i d'anada i tornada

Abstract

In this paper we review some of the fundamental properties of the free group and give a detailed account of Stallings's theory of automata, a geometric interpretation of its subgroups that has been (and still is) immensely fruitful, both as a means of understanding classical results, as as a source of new results. We review some of the most important ones. -- - En aquest article revisem algunes de les propietats fonamentals del group lliure i fem una exposici\'o detallada de la teoria dels aut\`omats de Stallings, una interpretaci\'o geom\`etrica dels seus subgrups que ha estat (i segueix essent) immensament fruct\'ifera, tant com a mitj\`a per entendre resultats cl\`assics, com com a font de nous resultats. N'expliquem alguns dels m\'es rellevants.