The clause "that I found in my book" is a relative clause, specifically an adjective clause. It provides additional information about the noun "book" by describing which book the speaker found.
Adverb clause
Noun.
adjective
adverbial clause
adverbial clause
This is a type of introductory clause that is called a dependent clause. It is basically one that help to provide some background information.
adverb
adjective
adverb
adverb
The clause is an adverb.
adjective