The document discusses the rules for using infinitives versus gerunds (verbs with "-ing") after other verbs in sentences. The main rule is that the second verb is usually an infinitive with "to", but there are many exceptions. Some key uses of the infinitive are after adjectives, to express purpose, and after certain verbs like "want". The gerund is used as a subject, after prepositions, and after certain verbs like "stop". Infinitives can also occur without "to" after modal and other verbs like "make" and "let".