We make here a few references to the Holy Spirit, of Whom we have about 55 in this book. The Lord Jesus had previously said, according to the Gospel of John: "And I will pray the Father, and He will give you another Helper, that He may abide with you forever" (14:16); "But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you." (14:26); "... He will testify of Me" (15:26); and "Nevertheless I tell you the truth. It is to your advantage that I go away; for if I do not go away, the Helper will not come to you; but if I depart, I will send Him to you" (16: 7).
The book of Acts has as the central character the Holy Spirit, the Helper, sent by the Father in the name of the Son. His are the "acts" focused on the book. The third Person of the Trinity is here to stay forever with the disciples of the Lord Jesus, not transiently as before as we see in the Old Testament. We understand that His task will only be completed when the church of Christ is raptured to meet the Lord in the air, before His second coming.
The Father, according to the request of the Son, made the promise of the Holy Spirit: not as inferior but equal with the Father. He would come in the name of Christ, as His representative on earth. He would not come to glorify Himself, but to testify of Christ. This is why the Holy Spirit does not lead us to give praise and worship to Himself, but to God the Father and Son.
He would come to teach us "all things" - He did this through the ministry of the apostles, reminding all that the Lord Jesus had said. Everything was recorded in God's written Word, the Bible, which we still have in our hands: it consolidates all His teaching, and should not be reduced, changed or increased. Men wrote it, but the Holy Spirit inspired it in its entirety.
The Lord commanded the apostles not to leave Jerusalem, after His ascension, until that promise was fulfilled. He reminded them that John (the Baptist) was baptized with water, but they would be baptized with the Holy Spirit (as foretold by John, Luke 3:16).
In their expectancy of the Messianic kingdom on earth, and as He had said before "All authority has been given to Me in heaven and on earth" (Matthew 28:18), the apostles were curious to know whether if it would be at this time that the Lord would restore the kingdom to Israel. In response, the Lord explained that the Father has an established programme, but it was not for them to know what they asked. The important thing now was to know that the Holy Spirit would come upon them, they would receive power, and be witnesses of the Lord Jesus Christ all over the earth, beginning from Judea and Samaria.
4 And being assembled together with them, He commanded them not to depart from Jerusalem, but to wait for the Promise of the Father, "which," He said, "you have heard from Me;
5 for John truly baptized with water, but you shall be baptized with the Holy Spirit not many days from now."
6 Therefore, when they had come together, they asked Him, saying, "Lord, will You at this time restore the kingdom to Israel?"
7 And He said to them, "It is not for you to know times or seasons which the Father has put in His own authority.
8 But you shall receive power when the Holy Spirit has come upon you; and you shall be witnesses to Me in Jerusalem, and in all Judea and Samaria, and to the end of the earth."
Acts chapter 1, verses 4 to 8