Present participles and the gérondif

The present participle ends in -ant and never agrees: les étudiants ayant fini peuvent partir. It replaces qui plus a verb in formal writing: une femme parlant trois langues.

The gérondif is en plus the present participle. It tells how or when, and its subject is the subject of the sentence: il travaille en écoutant de la musique, en arrivant, j'ai vu Paul.

Build it from the nous form of the present: nous finissons gives finissant. Three are irregular: étant, ayant, sachant. Do not confuse -ant with the adjective in -ent: en négligeant, but négligent.