The participle ascribes some fact, quality, or characteristic to the noun, or designates the noun as belonging to a general class
The participle like the adjective may modify the noun in the attributive relation. This construction may occur without an article. John 1:9
The participle may be used like an adjective in the predicate, after a verb of being.
When the participle is not accompanied by a noun it may function as a noun. This construction may be found with or without the article. It may be used as subject, object, or modifier

The participle may denote an affirmation that distinguishes the noun which it qualifies as in some way specially defined, or marked out in its particular identity.

Purpose may be denoted by the participle.

The Participle is used in the sense of a temporal clause, where it may be translated in English by when, after, or while.

The Participle may denote that which is the grounds for action in the main verb. Here it functions in the same general relation as a causal clause introduced by because or since.

The participle may function as the protasis of a conditional sentence.

The participle may denote a sense of concession, being used either with or without the concessive particle.

The participle may indicate the means by which the action of the main verb is accomplished.

The participle may signify the manner in which the action of the main verb is accomplished. This use of the participle may be accompanied by ὡς.

The participle may be used to complete the idea of action expressed in the main verb. When so used, it may modify either the subject or object of the verb and agree with it in case.

The participle may express an attendant circumstance – an additional fact or thought, which is best rendered in English by the conjunction “and” with a finite construction.

The participle may be used as an Imperative denoting urgency or a command.

Ordinarily expressed by the Aorist or Perfect

Ordinarily expressed by the Present (may be expressed by the Aorist)

Regularly expressed by the Future (may be expressed by the Aorist)

The Present tense of εἰμί with the Present Participle. This construction marks clearly the force of the continuing action.

The Imperfect tense of εἰμί and the Present Participle.

The Future tense of εἰμί and the Present Participle.

The Present tense of εἰμί and the Perfect Participle.

The Imperfect tense of εἰμί and the Perfect Participle.

The Future tense of εἰμί and the Perfect Participle.