Introduction
The Commissioning of the Apostles is the last scene that Matthew gives us in his gospel. There is no account of an Ascension here since Jesus tells his disciples "I will be with you always.1" Rather, the Ascension is already a past event, occuring in the Resurrection. In Matthew's gospel, this is the first time that Jesus appears to his disciples after rising from the dead (see 28:10). The setting of the narrative is a mountain in Galilee which had been pointed out to them by Jesus earlier (v.16). Below is an outline of the narrative
16 ... At the mountain of the Commissioning
17 ... The reaction of the disciples upon seeing Jesus
18-20 The Commissioning
18 ... All authority has been given to me
19-20a ... Make disciples of all nations
20b ... I am with you always
At the Mountain of the Commissioning
The commissioning is made on a mountain in Galilee. In Matthew's gospel, Galilee is the privileged place where the Light of Salvation of shines. It is from there too that it would spread its rays of light to the world. Luke makes Jerusalem the place from which the salvation seen by men is proclaimed throughout the world. This is a matter of differences in emphasis and theology.
Mountains are places of God's self-manifestation. In the Gospel of Matthew, Jesus proclaims the "constitutions" of the kingdom on a mountain (Mt. 5:1). It is also on a mountain where Jesus gives his disciples a preview of his resurrection glory (17:1). It was on that mountain where Jesus touched his disciples (17:7).
The Reaction of the Disciples
The disciples were divided upon seeing Jesus, that is, that some worshipped but others disbelieved. In Luke 24:41, the disciples are characterized having mixed feelings: overjoyed, they could not believe. The mixed reaction is normal for people who are experiencing something abnormal.
The disbelief of the disciples is one of the proofs of the credibility of the Resurrection. Earlier in Matthew's resurrection account, the soldiers who kept watch at the tomb of Jesus were instructed by Temple authorities to spread the word that Jesus' body has been snatched by his disciples (28:13). It is a story that still circulated during the time of the writing of Matthew's gospel (28:15). An account that admits the disbelief of the disciples, especially when these are the ones commissioned by Jesus himself, is an honest account of things as remembered. (See also Catechism of the Catholic Church, par. 644)
The Words of the Commissioning
The words of the commissioning can be divided into three ideas that are interlocked. The first idea is about Jesus' authority, the second is that the disciples share their discipleship with all the nations and lastly, that Jesus will always be with them.

Jesus begins the commissioning by declaring that all authority has been given to him by the Father. In a different way, Paul expresses the same idea when he writes that Jesus has inherited the Name above all Names (Phil. 2:11). Jesus is the Danielic Son of Man (cf. Daniel 7:14)
There was given him dominion, and glory, and a kingdom, that all the peoples, nations, and languages should serve him: his dominion is an everlasting dominion, which shall not pass away, and his kingdom that which shall not be destroyed
The second part of the commissioning is an instruction for spreading the news of this kingdom and calling in the peoples of all nations to be under His reign.
Make Disciples ... Baptize ... Teach

The words of commissioning proper are found between two pronouncements of Jesus about himself. "I have received all authority" on the one hand, and "I will be with you always" on the other. This makes the command to the disciples dependent upon the Lordship of Christ and his abiding presence. Second, the command "Go forth" looks like the commands given to Adam and Eve at the beginning of creation, and to Noah's family at the end of the Great Flood. While in Genesis the imperative "go forth" is connected to biological generation, here it is in the context of the spreading of Christ's reign. The act of "making disciples" is expressed as "baptizing" and "teaching". And both are directed "to all nations".
The mission to the Gentiles has been intimated by Matthew from the beginning of his gospel in the visit of the Magi at Jesus' birth (2:1-12), in Jesus' beginning his ministry in Galilee of the Gentiles (4:15), in those who came to him for healing (4:25), in the healing of the centurion's slave (8:5-13), in a saying about disciples under persecution being brought before Gentiles (10:18), his going to the region of Tyre and Sidon and his miracle for the Syro-Phoenician woman (15:21-28), in the parable about the wedding banquet (22:1-10), the saying about the gospel being preached to all the world (24:14), in the parable of the King (25:32) and his saying about the woman who anointed him (26:13). Jesus command to make disciples of all nations begins the realization of his words, especially as found in 24:14, 26:13 and 10:18.
"Baptizing" and "teaching" are tied up together as the disciples' realization of the command "make disciples of all nations." In modern parlance, we would speak of initiation into the mysteries and formation. "Teaching" in the early Church would take the form of two activities, "kerygmatic proclamation" for outsiders, "catechesis" for the initiated.
Baptizing into (eis)...
The disciples are instructed to baptize "into" the name of the Father, Son and Holy Spirit. The Greek preposition is used here. It has a dynamic meaning as opposed to "in" (en). The preposition is used with this meaning in the about 200 times it is used in the Gospel. This dynamic meaning of "eis" used in the already familiar baptismal formula (perhaps reaching back to Matthew's community itself) seems to indicate that those baptized in the name of the Trinity is in a way put into a dynamic relationship with "The Name"2.
"The Name" is one of the designations of "God" even among Jews of the present day. They call Him "The Name" because of the second commandment. In Matthew, "The Name" is given three designations: Father, Son and Holy Spirit. Catholics, Orthodox and mainline Protestants call this designation "The Trinity". For the Christian, God is Father, Son and Holy Spirit. They are baptized into the life of "The Name" which they recognize as Father, Son and Holy Spirit.
I am with you...
With the final words of the commissioning and of Matthew's gospel is the assurance that Jesus will not leave his disciples. The declaration creates an inclusion with the quote from Isaiah used by Matthew on the occassion of the Anunciation to Joseph (1:23). He is "Immanu-el", God-with-us. Like the Shekinah glory that accompanied the Israelites in the desert, Jesus will be covering his disciples as they go about doing his commands, baptizing and teaching all nations.
1. There is something similar here to John's account of the aapearance to the disciples on the evening of that first Sunday. There, he had already ascended to the Father and was coming (from heaven) bringing with him the gifts of the Holy Spirit. If one thinks that the scene is about the Ascension of Jesus this is probably more due to Hollywood. In the movie "Greatest Story Ever Told", Jesus (played by Max von Sydow) recites Matthew 28:18-20 as he ascends to the heavens.
2. The dynamic nature of baptism indicates that the baptized cannot be reduced to mere numbers on baptismal records. It is for this reason that the command "teaching them all that I commanded you" goes hand in hand with the command to baptize. Initiation and formation go together.

