Acts 1:1

The former treatise have I made
Meaning the Gospel written by him the Evangelist Luke, for from that he makes a transition to this, beginning here where he there left off; namely, at the ascension of Christ; see ( Luke 24:51 ) .

O Theophilus; (See Gill on Luke 1:3)

of all that Jesus began both to do and teach.
This is a summary of his former treatise, his Gospel, which gave an account of what Christ began to do, and did; not of the common and private actions of his life; or of what was done, either in public, or private, throughout the whole of his life; for excepting that of his disputing with the doctors at twelve years of age, no account is given by him of what he did, till he was about thirty years of age; but of his extraordinary actions, of the miracles he wrought; and these not all, and everyone of them; but many of them, and which were sufficient to prove him the Messiah; and particularly of all things he did relating to the salvation of his people; of the whole of his obedience; of his compliance with the ceremonial law; of his submission to baptism; of his holy life and conversation, and entire conformity to the law; of his sufferings and death, how that thereby he made full atonement for sin, brought in an everlasting righteousness, and obtained eternal redemption for his people: and not only Luke, in his Gospel, gave an account of these his actions, but also of many of his excellent discourses, his parables, and his sermons, whether delivered to the people in common, or to his own disciples: and now, as this was the subject of his former book, he intended in this latter to treat, as he does, of what the apostles of Christ began to do and teach.