1:1 Theophilus. The “former treatise” is clearly the gospel of Luke, both books being addressed to “Theophilus” (a name meaning “lover of God”). If Theophilus is not a generic name for anyone who is a lover of God, then the reference is evidently to a Roman official (as indicated by the adjective “most excellent” in Luke 1:3) in whom Luke had special interest, either seeking to lead him to Christ or to build him up in his newfound Christian faith.
1:1 Jesus began. Luke’s gospel contains the record of what Jesus began to do and teach. The implication is that Luke’s supplementary treatise tells what He continued to do and teach through the apostles by the enabling power of His Spirit, whom He sent to indwell and guide them at Pentecost.