The Easter Vigil includes the Liturgy of baptism with the blessing of baptismal water and the renewal of baptismal promises. The very placement of this liturgy reminds us of St. Paul's teaching that baptism involves dying with Christ and rising to a new life, symbolized dramatically in baptism by immersion.
In the Letter to the Galatians Paul was arguing against some Christian Jews who insisted that to be saved, Gentiles must observe all the Jewish laws including those external works that distinguish Jews, such as circumcision of males. Paul's response to this was to first establish his authority, including the approval of Peter and James. Then, Paul clearly taught that one is not declared righteous by God, justified, saved, through "works of the law" but by faith in/of Jesus. The "in/of" regarding this faith has recently been brought forth as an important distinction.
Chapter 2 of Galatians contains the core of Paul's thoughts on this "faith." In 2:16 one finds "... we have believed in Christ Jesus, in order to be declared righteous by faith in/of Christ." This holds that we have believed in Christ Jesus, in who he is, what he has done for us and all that he teaches in the gospels. One profoundly understands that Jesus' way of life is the way of life intended by God.
What of the "faith in/of Christ?" The most recent study of the two words "faith" and "Christ" in the Greek stress that there is have no word for "by" or "of," either could hold. But the context of Paul's use of these words implies that we should read "faith of Christ."
The key verse in this regard is 2:20, "I have been crucified with Christ; it is no longer I who live, but Christ who lives in me: the life I now live in the flesh I live by the faith of/in the Son of God, who loved me and gave himself for me."
"I have been crucified with Christ" is a reference to baptism as dying and rising with Christ. Paul follows this with "it is no longer I who live, but Christ who lives in me." Christ living within him allows Paul to conclude: "the life I now live in the flesh I live by the faith of the Son of God who loved me and gave himself for me." Paul implies that the faith of the Son of God is within him; God's Son's faith is what he lives by. Finally, "who loved me and gave himself for me" is a reference to the death of Jesus.
One can conclude that through baptism, one is gifted to live by the faith of Jesus, to practice and develop the "type of faith" that Jesus practiced in worship and ethical behavior, knowing that Jesus' faith led to his death and accepting to do the same. Remembering that Jesus was fully human in all but sin (Hebrews 4:15) and experienced the real trials of human life without detailed knowledge of the future, his life of faith teaches us the way to God.
Then from verse 2:16 we understand that living by the faith of Jesus we resemble him and therefore are and will be declared by God to be blameless, upright, saved. From Paul's understanding, this is what we have done in baptism and what we pledge to do when we renew our baptismal promises, not just recite words of the creed, words of belief, but live the faith Christ himself displayed in his earthly life. We believe in Jesus Christ and live the faith of God's Son, Jesus.