10:1 There was a certain man in Caesarea called Cornelius, a centurion of the band called the Italian band,

10:2 A devout man, and one that feared God with all his house, which gave much alms to the people, and prayed to God alway.

Cornelius was a Gentile, but, he was devout to the Lord.

10:5 And now send men to Joppa, and call for one Simon, whose surname is Peter:
He was told to send for Peter.

10:11 And saw heaven opened, and a certain vessel descending upon him, as it had been a great sheet knit at the four corners, and let down to the earth:

Peter had a vision of the Lord and was told that what the Lord had said was clean should not be seen as otherwise. The Lord was talking of Gentiles, no longer being deemed as unclean.

The book of Acts is a transitional book; it moves from the old economy of the Law to the dispensation of Grace; it moves from the diminishing of Israel toward the Gentiles. It moves from the twelve to Paul.

10:24 And the morrow after they entered into Caesarea. And Cornelius waited for them, and he had called together his kinsmen and near friends.

10:34 Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons:

Peter spoke to those gathered, consisting of Jews and Gentiles.

10:35 But in every nation he that feareth him, and worketh righteousness, is accepted with him.

10:36 The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all

Jesus is Lord of all, but he went first, to the house of Israel.

10:37 That word, I say, ye know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached;

10:38 How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing all that were oppressed of the devil; for God was with him.

10:39 And we are witnesses of all things which he did both in the land of the Jews, and in Jerusalem; whom they slew and hanged on a tree:

Here Peter is accusing Israel, once again, in slaying Jesus.

10:40 Him God raised up the third day, and shewed him openly;

10:41 Not to all the people, but unto witnesses chosen before God, even to us, who did eat and drink with him after he rose from the dead.

Peter is confirming the resurrection.

10:42 And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead.

This is the "great commission", which can be noted, was not given to the Body of Christ, but to the Apostles. The Body of Christ is to be the ambassadors of Christ, pleading for all to be reconciled to God thru faith in Christ.

10:43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.

Peter is not preaching the cross here, he is preaching faith in the name of Jesus for the remission of sins.

10:44 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.

10:45 And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost.

The Gentiles believed and received the Holy Ghost, just as the Jews had.

10:46 For they heard them speak with tongues, and magnify God. Then answered Peter,

10:47 Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?

10:48 And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.

Peter, preaching the Gospel of the Circumcision, commanded baptism under the program of Israel.