In Sacred Bond; Covenant Theology Explored the authors, Michael G. Brown and Zach Keele, lay the ground work and define the Covenant of Redemption (or pactum salutis) as follows:
The covenant of redemption is the first of three overarching covenants in redemptive history, namely, the covenant of redemption, the covenant of works, and the covenant of grace…. Sometimes referred to by its Latin title, pactum salutis, the covenant of redemption is the origin and firm foundation of the covenant of grace. Without it, there would be no election, no incarnation of the Son, no cross, no resurrection, and no promise of heaven. In short, there would be no salvation of sinners.
The covenant of redemption is unique for at least two other reasons. First, it was made between the persons of the Trinity, and not, as in most biblical covenants , between God and humans. The covenant of redemption is a pact between the Father, the Son, and the Holy Spirit with the purpose of redeeming God’s elect. The Father gave to the Son those whom he chose to save and required him to accomplish their salvation th[r]ough his obedient life and atoning death as the second Adam. He also promised the Son a reward on the completion of his work. The Son accepted the Father’s gift, agreed to the conditions of this covenant, and submitted himself to the Father’s will. The Holy Spirit promised to apply the benefits earned by the Son to the elect and unite them with the Son forever. Thus, we say the covenant of redemption is an intratrinitarian covenant between the Father, Son, and Holy Spirit.
Second, the covenant of redemption is unique because it was established before time. All other biblical covenants were made in time and history. The covenant of redemption, however, was made in eternity, before the foundation of the world and all things temporal. Thus, we say that it is a pretemporal covenant.
Therefore, behind all of God’s covenanting with Adam, Noah, Abraham, Israel, David, and his elect, stands the covenant of redemption. Planned from eternity by the members of the Godhead, the covenant of redemption is the basis and driving purpose of all redemptive history. We give a summary definition of the covenant of redemption as the covenant established in eternity between the Father , who gives the Son to be the Redeemer of the elect and requires of him the conditions for their redemption; and the Son, who voluntarily agrees to fulfill these conditions; and the Spirit, who voluntarily applies the work of the Son to the elect. (pp. 24-25 in the book).
Brown, Michael G.; Keele, Zach (2012-05-29). Sacred Bond; Covenant Theology Explored (Kindle Locations 310-330). Reformed Fellowship, Inc.. Kindle Edition.
This summary is typical among Reformed theologians of the seventeenth century. They understood Scripture to teach the covenant of redemption as one of obedience and obligation for Christ. Forgiveness of sins and eternal life for the elect was possible only by Christ fulfilling the demands of God’s justice through his life of obedience and death of atonement. Thus, Christ became the covenant-keeper in whom we place our trust for salvation. Owen also pointed out that the Holy Spirit has an essential role in the covenant of redemption. It was through the Holy Spirit that the Virgin Mary conceived the incarnate Christ, Christ offered himself to the Father, and he was raised from the dead. Moreover, the Holy Spirit is also responsible for bringing the elect into union with Christ and keeping them secure. Our salvation is Trinitarian from beginning to end. (pp. 34-35 in the book).
Brown, Michael G.; Keele, Zach (2012-05-29). Sacred Bond; Covenant Theology Explored (Kindle Locations 490-517). Reformed Fellowship, Inc.. Kindle Edition.
This book is perhaps the best introduction to covenant theology I have read. I highly recommend it. It is available for purchase here: Sacred Bond; Covenant Theology Explored