This is a simplified commentary on Acts 1. This is not a completed work and will be updated as needed. Also note, commentaries come from human views and reasoning. Study carefully.
The former account I made, O Theophilus, of all that Jesus began both to do and teach,  until the day in which He was taken up, after He through the Holy Spirit had given commandments to the apostles whom He had chosen,  to whom He also presented Himself alive after His suffering by many infallible proofs, being seen by them during forty days and speaking of the things pertaining to the kingdom of God.Acts 1:1-3 NKJV
The name, Theophilus (lover or friend of God), links the Gospel according to Luke and the Book of Acts. The writer starts by mentioning his first book, quickly summarizing his work over the life of Jesus.
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;  for John truly baptized with water, but you shall be baptized with the Holy Spirit not many days from now.”  Therefore, when they had come together, they asked Him, saying, “Lord, will You at this time restore the kingdom to Israel?”  And He said to them, “It is not for you to know times or seasons which the Father has put in His own authority.  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.”  Now when He had spoken these things, while they watched, He was taken up, and a cloud received Him out of their sight.  And while they looked steadfastly toward heaven as He went up, behold, two men stood by them in white apparel,  who also said, “Men of Galilee, why do you stand gazing up into heaven? This same Jesus, who was taken up from you into heaven, will so come in like manner as you saw Him go into heaven.”Acts 1:4-11 NKJV
The disciples were assembled together with Jesus. They are told to not leave Jerusalem until they receive the promise of the Father. The promise of the Father was the Comforter/Helper (John 14:16) and was promised to the disciples by Jesus (John 15:26). The Book of Acts helps to verify both gospels according to Luke and John. (Many of the same elements are contained within both books.) The term “promise of the Father” parallels what Luke had previously written, found in Luke 24:49.
Jesus explains that only after they receive power after they receive the Holy Ghost, will they then go out to all the world and preach the gospel. Power, this verse (Acts 1:8) likely refers to the signs that would follow true believers as mentioned in Mark 16:17-18. Power would not refer to speaking in tongues only, as speaking in tongues is only one sign and is not in continuity. Power here seems to be something of which would be an on-going process. God would commonly perform miracles via the power of the Holy Spirit residing in the disciples.
Then they returned to Jerusalem from the mount called Olivet, which is near Jerusalem, a Sabbath day’s journey.  And when they had entered, they went up into the upper room where they were staying: Peter, James, John, and Andrew; Philip and Thomas; Bartholomew and Matthew; James the son of Alphaeus and Simon the Zealot; and Judas the son of James.  These all continued with one accord in prayer and supplication, with the women and Mary the mother of Jesus, and with His brothers.Acts 1:12-14 NKJV
It is likely that this upper room is the same upper room mentioned in Acts 2 (the same people, in both number and name, were gathered together in this upper room on both occasions). These men and women were in one accord (and one mind) after the ascension of Jesus, and within ten days, the Holy Ghost would fall on them. Acts 2 would also mention the believers being of one mind and in one accord.
And in those days Peter stood up in the midst of the disciples (altogether the number of names was about a hundred and twenty), and said,  “Men and brethren, this Scripture had to be fulfilled, which the Holy Spirit spoke before by the mouth of David concerning Judas, who became a guide to those who arrested Jesus;  for he was numbered with us and obtained a part in this ministry.”  (Now this man purchased a field with the wages of iniquity; and falling headlong, he burst open in the middle and all his entrails gushed out.  And it became known to all those dwelling in Jerusalem; so that field is called in their own language, Akel Dama, that is, Field of Blood.)  “For it is written in the Book of Psalms: ‘Let his dwelling place be desolate, And let no one live in it’; and, ‘Let another take his office.’  “Therefore, of these men who have accompanied us all the time that the Lord Jesus went in and out among us,  beginning from the baptism of John to that day when He was taken up from us, one of these must become a witness with us of His resurrection.”  And they proposed two: Joseph called Barsabas, who was surnamed Justus, and Matthias.  And they prayed and said, “You, O Lord, who know the hearts of all, show which of these two You have chosen  to take part in this ministry and apostleship from which Judas by transgression fell, that he might go to his own place.”  And they cast their lots, and the lot fell on Matthias. And he was numbered with the eleven apostles.Acts 1:15-26 NKJV
Peter mentions Judas, the ex-disciple of Jesus that would lead soldiers to Jesus. Peter explains that another should take Judas’ place, so the believers found men that had been followers alongside them, and cast lots. The lot leads them to make Matthias an apostle among the eleven.