Theophilus

Who is "Theophilus" (Acts 1:1)?
Theophilus, whose name is Greek and means "loved of (philus) God (Theo)," was a gentile government official. The Bible contains two letters from Luke to Theophilus. His first is what we today call the Gospel of Luke. Luke's second letter to Theophilus is what we today call The Acts of the Apostles, and by the time he wrote it, Luke and Theophilus may have become better acquainted since Luke addresses him simply as "O Theophilus" (Acts 1:1) after having formally addressed him as "most excellent Theophilus" (akin to calling a high government official "Your Excellency" today) to begin his first letter to him: "Since many have taken in hand to set in order an account of the things that have been fulfilled among us, just as those who from the beginning were eyewitnesses and servants of the word delivered them to us, it seemed good to me also, having carefully investigated everything from the beginning, to write to you an orderly account, most excellent Theophilus, that you may know the certainty of the things about which you have been instructed." (Luke 1:1-4)

What does "taken up" (Acts 1:2) refer to?
Jesus' ascension to heaven, which we will read about shortly.

How long did Jesus remain on earth after His resurrection?
"forty days" (Acts 1:3).

How many people saw Him during those forty days?
"Over five hundred" as indicated in 1 Corinthians 15:3-6: "For I delivered to you first of all that which I also received: that Christ died for our sins according to the Scriptures, and that He was buried, and that He rose again the third day according to the Scriptures, and that He was seen by Cephas, then by the twelve. After that He was seen by over five hundred brethren at once, of whom the greater part remain to the present, but some have fallen asleep."

What else did Jesus do besides "being seen by them" (Acts 1:3) during those forty days?
He spoke to them "of the things pertaining to the kingdom of God" (Acts 1:3). He walked with them: "Now behold, two of them were traveling that same day to a village called Emmaus, which was seven miles from Jerusalem. And they talked together of all these things which had happened. So it was, while they conversed and reasoned, that Jesus Himself drew near and went with them" (Luke 24:13-15). He ate in front of them - When He had said this, He showed them His hands and His feet. But while they still did not believe for joy, and marveled, He said to them, “Have you any food here?” So they gave Him a piece of a broiled fish and some honeycomb. And He took it and ate in their presence. (Luke 24:40-43) -  as well as with them and even cooked them breakfast (see John 21:9-14 in Jesus). So it wasn't just some vision that the people saw. Jesus physically spent time with them.

Is there any other evidence of Jesus' resurrection?
See Resurrection of Jesus.