Translation from the book:

Στεργίου Ν. Σάκκου, Ἑρμηνεία στό κατά Λουκᾶν Εὐαγγέλιο, τόμ. Α΄, 

ἐκδ. «ΧΡΙΣΤΙΑΝΙΚΗ ΕΛΠΙΣ» ΟΡΘΟΔΟΞΗ ΑΔΕΛΦΟΤΗΤΑ, Θεσ/νίκη 2008, σσ. 154-159

(Stergios N. Sakkos [Read CV], A Commentary on the Gospel according to St. Luke, vol. A', pp. 154-159)

  In the Gospel according to Luke, the event of Jesus' baptism is briefly recounted. This description, however, provides more information which the other evangelists do not give (see Mt 3:13-17; Mk 1:9-11; Jn 1:32-34). These distinctive events are:
  a) Jesus came to John to be baptized after all the people had already been baptized.
  b) Jesus prayed at the time of baptism.
  c) The Holy Spirit came down “in a bodily form, like a dove” (v. 22).

3,21. Ἐγένετο δὲ ἐν τῷ βαπτισθῆναι ἅπαντα τὸν λαὸν καὶ Ἰησοῦ βαπτισθέντος καὶ προσευχομένου ἀνεῳχθῆναι τὸν οὐρανόν.
3:21 Now when all the people were baptized, and when Jesus also had been baptized and was praying, the heaven was opened.

  The expression “all the people” does not mean that all the people of Palestine were baptized, but that John's preaching was made known everywhere, so that all those who wanted to be baptized, they were baptized. Jesus also wanted to be baptized like the rest of the people. All the others, of course, confessed their sins first; Jesus immediately came out of the waters of the Jordan (see Mt 3:16; Mk 1:10), because he was sinless. He had no need of purification, but he accepted baptism in order to keep the whole law, as he explained to the Baptist who vividly expressed his objections (cf. Mt 3:15).
  St John Damascene, referring to the theology of Jesus’ baptism, writes: "He is baptized, not as one who needs cleansing, but for my purification, that he may break the demons’ heads on the water, to drown the sin in the water, and to bury the old Adam in the water, to sanctify the baptizer, to fulfill the law, to reveal the mystery of the Trinity, to be a symbol and example for our baptism."
  The baptism of Jesus is another act of humiliation. The shock John experienced (see Mt 3:14) before this humiliation of the Lord is emphasized with very strong contrasts in the Doxastikon of the Great Consecration of the Epiphany; “The Forerunner was seized with trembling, and cried aloud, saying: “How can a lamp illumine the light? How can a slave lay his hand upon his Master?”
Zygavinos notes that at the time of his baptism Jesus prayed "teaching that those who are baptized should pray".

3,22. καὶ καταβῆναι τὸ Πνεῦμα τὸ Ἅγιον σωματικῷ εἴδει ὡσεὶ περιστερὰν ἐπ᾿ αὐτόν, καὶ φωνὴν ἐξ οὐρανοῦ γενέσθαι λέγουσαν· σὺ εἶ ὁ υἱός μου ὁ ἀγαπητός, ἐν σοὶ εὐδόκησα.
3:22 and the Holy Spirit descended upon him in a bodily form, like a dove, and a voice came from heaven, which said, "You are my beloved Son; I am well pleased in you."

  During the Lord's baptism, before people’s astonished eyes, the heaven was opened as if it had been torn (see Mk 1:10). From the open heavens the Holy Spirit descended “like a dove” and stood upon Jesus. Thus, John was assured that Jesus was the expected Messiah, according to the information he received from God Himself (see Jn 1:33). The people who were standing by also understood to whom the voice that was heard afterwards, referred to.
  The third person of the Holy Trinity appeared “in a bodily form” like a dove. He appeared “εἴδει”, that is, in appearance, not in the nature of a dove. He did not become a real dove, he was not incarnated, but he appeared in this way so that people could see him. In other words, it did not happen the same as to the Son, who took human nature and, as the evangelist John notes, “the Word became flesh” (1:14).
  The dove symbolizes integrity, meekness and peace. The Holy Spirit was revealed in the form of the dove "that we may know we must be meek and pure", underlines St. Theophylact. The dove also signifies Jesus’ sinlessness and his work of peace, by which he would reconcile the earth with heaven. St. Chrysostom recalls that also in Noah's ark a dove came bearing an olive branch, a symbol of God's love for man and of the deliverance from his sufferings. At the Lord’s baptism, according to the same father, the Holy Spirit came in the form of a dove to announce God’s mercy to the world.
  The Father’s voice was also heard from heaven, giving his testimony concerning Jesus, "You are my beloved Son; I am well pleased in you." In the Homeric and classical Greek language, “beloved” often means "only-begotten", hence, of the same nature. The verb “εὐδoκω” means "to be pleased, to feel relieved, to feel pleased ". In this case the Father's pleasure is absolute, because the Son is of the same nature with the Father. He is the one who reveals the Father’s person to the world, “the express image of his person” (Heb 1:3). “He who has seen me has seen the Father” (Jn 14:9), said the Lord to his disciple Philip shortly before the Passion.
  The triune God was revealed in Jesus’ baptism; the Son was baptized in the waters of the Jordan, the Holy Spirit descended in the form of a dove and the presence of the Father was sensed in the voice that was heard. This truth is conveyed in the Apolytikion of the feast of the Epiphany: "When You were baptized in the Jordan, O Lord, the worship of the Trinity manifested; for the voice of the Father bore witness to You, calling You His beloved Son. And the Spirit in the form of a dove, confirmed the certainty of the word. O Christ our God, who has appeared and has enlightened the world, glory be to You”. This complete revelation of the triune God will be repeated in the Transfiguration of Jesus the Saviour (see Mt 17:1-8; Mk 9:2-8; Lk 9:28-36).
  By the baptism Christ was formally enthroned on three thrones:
  a) on the throne of the Teacher; to teach the truth of his gospel,
  b) on the throne of the high priest, to celebrate the great sacrifice, in which he would be at the same time both the sacrificial priest and the prey, the lamb “Behold the Lamb of God, which has taken away the sin of the world” (Jn 1:29),
  c) finally, on the throne of the King, because he is the King of the eternal kingdom, his Church, to which belong all those who had been disciples by his teaching and they were redeemed by his sacrifice.

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