What New Testament book tells of the work of the early church?

Answer 1

Acts of the Apostles has long been regarded as a history of the early Church.

The Acts Seminar was set up to review the book carefully and look for evidence of historicity in Acts. It determined that the book was written in the second century and does not accurately record events at the time of the early church. Scholars participating in the Seminar concluded (See Acts and Christian Beginnings) that Acts is "a primary resource for understanding second-century Christianity", as the book writes of events and purported events in the time of Peter and Paul as if they took place at the time of writing.

Answer 2

The book of the Acts of the Apostles concentrates on this. Other books contain primarily teaching although they do have incidental historical references to people and places.