The primary witnesses were His apostles who lived with Him during His ministry. They also witnessed His departure and the promise of His return.
As [the apostles] were looking on, He was lifted up, and a cloud took Him out of their sight. And while they were gazing into heaven as He went, behold, two men stood by them in white robes, and said, “Men of Galilee, why do you stand looking into heaven? This Jesus, who was taken up from you into heaven, will come in the same way as you saw Him go into heaven.” (Acts 1:9-11)
Moments before His ascension, Jesus had instructed them,
You will receive power when the Holy Spirit has come upon you, and you will be My witnesses in Jerusalem and in all Judea and Samaria, and to the end of the earth. (Acts 1:8)
That commission becomes the outline of Acts, the history of the early church. Terrified apostles, who had abandoned Jesus during His trials, suddenly became courageous proclaimers of Christ in the face of deadly persecution. Why? Because they had seen Jesus’ victory over death, and they were empowered by His Spirit! Their Good News spread like wildfire in a dry forest, igniting first in Jerusalem, then jumping to Judea and Samaria, then spreading to distant lands—all within about 30 years. That is the history recorded by Acts.
Luke, a medical doctor, wrote the Gospel account called Luke and its sequel Acts. The content of each book reveals its purposes. Acts shows the continuing work of Jesus (Acts 1:1). By His Spirit, He began building His church, just has He had promised (Matthew 16:18). Acts is important for anyone wanting to belong to Christ. In case after case, it shows how people of all kinds must respond to the Lord to be saved and added to His church (Acts 2:41, 47; 9:31). Acts continues the kingdom theme (Acts 1:3; 8:12; 14:22; 19:8; 20:25). It uses Paul’s trials to prove that followers of Christ are law-abiding citizens, and not subversive to earthly rulers (Acts 22-26 cf. John 18:36).