An "infinitive" in English is a verb preceded by the word to, as in to study. Many English verbs can be followed by a grammatical structure that contains an infinitive and is known as an "infinitive ...
The most common use of the perfect infinitive is to say ‘after having done’ something. Après avoir fait mes devoirs, j’ai regardé la télé. – After having done/After doing my homework, I watched TV.