Generations and genealogy of Jesus:
The genealogy of Christ opens with a statement similar to the various divisions of the Book of Genesis{showing the unity of the scriptures}. Jesus Christ is the Title most often used of the Saviour. Jesus{Gr. Iesous; Heb. Yehoshua}is his earthly name.
Christos is the Greek translation for ,"Messiah" or "Anointed", or Jesus the Christ.
Son of David:Tracing Jesus' ancestry back to King David through the line of Davidic Kings, Matthew connects Jesus' with his royal heritage. The genealogy here is that of Joseph, Jesus' legal father. Whereas the genealogy of Luke 3:23-28 is that of Mary, His actual parent,showing his bloodline back to David.
The authors purpose is to show that the messianic promises made to David's line are fulfilled in Jesus.
Son of Abraham: He is also the fulfillment of the covenant promises to Abraham, the forefather of the Jews{Gen. 12:3;13:15;22:18}.
Since Matthew is writing primarily to Jewish readers, he naturally begins by emphasizing Jesus' Jewish parentage.
God Bless!