Non - Finites
Non-finite is a form of verb that does not display a distinction in tense, in contrast with a finite verb, where there is a distinction between present tense and past tense. Eg. hopes, hoped. A non-finite verb is either infinitive, participle or gerund.
The infinitive is the base of a verb, often followed by 'to' as;
1. To err is human.
2. Birds love to sing.
In sentence one the infinitive like a noun is the subject of the verb 'is'.
In sentence two the infinitive like a noun is the object of the verb 'love'.
After certain verbs like bid, let etc we use the infinitive without 'to' as;
1. Bid him go there.
2. Let him sit here.
A participle is a word, which is partly a verb and partly an adjective.
In the sentence
Hearing the noise the boy woke up,
The phrase hearing the noise, which is introduced by a participle, is called a participle phrase and according to the latter part of the definition, it is an adjective phrase.
A gerund is that form of the verb, which ends in -ing and has the force of a noun and a verb.
As both, gerund and the infinitive have the forces of a noun and a verb, they have the same uses.
Thus in many sentences, either of them may be used without any special difference in meaning such as;
Teach me to swim.
Teach me swimming.
To give is better than to receive.
Giving is better than receiving.