From Teflpedia

An infinitive, is a type of verbal that isn’t a participle. As a non-finite verb form, it lacks finiteness, which basically means that either it lacks a subject or it is a subject. There are two infinitives in English; a bare infinitive and a to-infinitive. Somewhat confusingly, either of these may be referred to simply as "the infinitive" without further specification.

Name Examples Notes
Bare infinitive He made me do it!

We can do it!

To infinitive I want to go to the park.

To complain would show disrespect.

The infinitive is identical in form to the base form, however the base form is finite as it always has a subject (though this may be an implied subject, especially in imperative mood).

In most other languages related to English, there is only a single infinitive is a single word, e.g. "to play" is "jouer" in French. Hence the prescriptivist split infinitive rule.

Infinitives can express aspect; a perfect infinitive is has the form "to have done something" while a progressive infinitive is "to be doing something".

Full modal verbs do not have infinitives. For example one cannot say *"to can"; one would have to employ a different way of achieving the same task, e.g. by using "to be able to" or "to be allowed to". See infinitive of a modal verb.