Two examples of Gerunds here.
We use the bare infinitive (the infinitive without 'to'):
We use gerunds (verb + ing):
Two examples of Infinitives here.
We use 'to' + infinitive:
Examples: 1. She agreed to give a presentation at the meeting. 2. We decided to go out for dinner.
-After prepositions. -As the subject or object of a sentence.
Examples: 1. I enjoyed living in France. 2. I fancy seeing a film tonight.
-After many adjectives. -To show purpose.
-After modal verbs. -After 'let', 'make' and (sometimes) 'help'. -After some verbs of perception (see, watch, hear, notice, feel, sense).