What is the perfect participle?

The perfect participle is a verb form used to indicate completed action, or to show that an action is ongoing.

You form the perfect participle by putting the present participle having in front of the past participle.

For example:-

having done, having finished, having read, having spoken

It can be used to form the passive voice.

For example:-

Having improved her English Pia's promotion prospects were much better.

Here is a comprehensive list of irregular verbs.