NOT HAVING BEEN INVITED to the wedding, he didn't come.
Perfect participle - Passive adverbial clause of reason/result: Because he hadn't/As a result of not having been invited to the wedding, he didn't come.
OPENING the door, she saw me.
Present participle, adverbial clause of time: When she opened the door, she saw me.
What I really like is TRAVELLING to other countries.
Gerund. It functions as a noun.
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