The former treatise have I made, O Theophilus, of all that Jesus began both to do and teach, The former treatise - The Gospel according to Luke, which is here most evidently intended.
O Theophilus - See the note on Luke 1:3.
To do and teach - These two words comprise his miracles and sermons. This introduction seems to intimate that, as he had already in his Gospel given an account of the life and actions of our Lord, so in this second treatise he was about to give an account of the lives and acts of some of the chief apostles, such as Peter and Paul.