VERSES 1-2: The former treatise have I made, O Theophilus, of all that Jesus began both to do and teach, Until the day in which he was taken up, after that he through the Holy Ghost had given commandments unto the apostles whom he had chosen: The former treatise that he is talking about is the Gospel of Luke which he had penned earlier to the same person, Theophilus. No one really knows for sure who Theophilus was. His name means lover or friend of God. In his Gospel, he wrote about all that Jesus began both to do and teach, Until the day in which he was taken up. Now, he is going to write about things that happened after the Lord's ascension.
Notice that Jesus had given commandments to the apostles whom he had chosen. What commandments had been given to them? Pick one. They are all contained in the Gospels of Matthew, Mark, Luke, and John. The bottom line is that all of these commandments had to do with the Kingdom that was at hand and had nothing to do with the age of Grace that would come instead.
VERSE 3: To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God: Apparently, during the 40 days between his resurrection and ascension, Jesus spoke to them the things pertaining to the kingdom of God. That means that Jesus had 40 days to explain to the eleven what was going on. As I stated earlier, they were no doubt caught off guard with the crucifixion. With that said, too many today erroneously think that the apostles were ignorant of what was going at Pentecost. No, not at all. They were fully aware of what was going on. In truth, the problem today is that most in the church do not realize what was truly going on in the first eight chapters of Acts. If they did, I assure you that it would change the church drastically because far too many teachings today rely upon a faulty understanding of these events.
Promise of the Father
VERSE 4-5: And, being assembled together with them, commanded them that they should not depart from Jerusalem, but wait for the promise of the Father, which, saith he, ye have heard of me. For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence. They were told not to depart from Jerusalem but to wait for the promise of the Father. What was that promise? The promise of the Holy Ghost as foretold in Joel 2:28-32 which says, And it shall come to pass afterward, that I will pour out my spirit upon all flesh; and your sons and your daughters shall prophesy, your old men shall dream dreams, your young men shall see visions: And also upon the servants and upon the handmaids in those days will I pour out my spirit. And I will shew wonders in the heavens and in the earth, blood, and fire, and pillars of smoke. The sun shall be turned into darkness, and the moon into blood, before the great and the terrible day of the LORD come. And it shall come to pass, that whosoever shall call on the name of the LORD shall be delivered: for in mount Zion and in Jerusalem shall be deliverance, as the LORD hath said, and in the remnant whom the LORD shall call. So, they were to await these events in Jerusalem. This point is too powerful to be overlooked with a casual reading. They were to wait for the outpouring of the Spirit as foretold by the Prophet Joel which would enable them to preach the Gospel of the Kingdom throughout the coming Tribulation which would culminate with the return of Christ and the establishment of the Kingdom as foretold by the Lord in Matthew 24:14.
Just a note at this point, if you have a red-letter edition of the Bible, you will notice that the entire phrase wait for the promise of the Father, which, saith he, ye have heard of me. For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence is in red letters. In actuality, Jesus never spoke these words. Instead, they were spoken by John the Baptist in Matthew 3:11 and Luke 3:16. Incidentally, the red-letter editions of the Bible did not come out until around 1899.
On another final note, the King James Version of the Bible always uses the term Holy Ghost when referring to the third person of the Trinity. This is done 90 times in the New Testament.