Preliminary point: please use proper punctuation. Note that sentences begin with a capital letter and end with some kind of terminal point: What is an adverbial phrase sentence starter?Can someone please give me an example?
Are you asking about the kind of construction found in examples like these?:
Having read the report, I can see what the problem is. All things considered, it was a reasonable result. His hands gripping the door, he let out a volley of curses.
The underlined expressions are called supplementary adjuncts in pre-subject position.
Note, by the way, that the term 'adjunct' is more appropriate than 'adverbial', and they are clauses not phrases.