From the Sacred Triduum Missal, published by Neri Publications and Opus Mariae Mediatricis:
This ceremony begins with the lighting of the new fire, symbolizing the eternal Trinity. From this fire is lit the paschal candle, which symbolizes the taking of a human nature by our Lord. After the exultant chant of "Lumen Christi" three times down the main aisle of the church, there follows the chanting of the Exsultet, which expresses the joy of the Church at the Resurrection of our Lord from the dead. This is followed by the chanting of the prophecies which review for us the fall of man from the state of grace and his need for redemption, something made all the more real if the sacrament of baptism is administered in conjunction with the blessing of the baptismal waters. Before the adding of the holy oils to the baptismal water, a sufficient amount is set aside for the renewal of baptismal promises and also for the faithful to take home as Easter Water after the Easter Masses, if so desired. Then follows the solemn Mass of the Paschal Vigil. Note that there is no Agnus Dei in this Mass at all, no doubt because we need not at this moment make the invocation "miserere nobis", as mercy has already been shown us, and once again the "dona nobis pacem" is not invoked of the Lord until we commemorate the giving of this gift which took place on the first Easter Sunday. This Mass ends with the chanting of Lauds after Holy Communion, during the Benedictus of which the altar is incensed. Also note the absolutely glorious chant, three-fold, of the Alleluia on a higher note each time, before the chanting of the Gospel.