How Many Covenants Are There in the Bible?

To simplify matters I am only going to address covenants with God rather than between human persons (e.g. David and Jonathan). Most scholars recognize five major covenants in the Bible.

1. Noahide Covenant: God established a covenant with Noah and his descendants to never again flood the earth destroying all life (Gen. 9:9). This covenant is established with all of humanity. Humanity is tasked with fulfilling seven commandments (do not worship idols, do not curse God, establish courts of justice, do not commit murder, do not commit sexual immorality, do not steal, do not eat flesh torn from a living animal).
2. Covenant with Abraham: God established a covenant with Abraham that he would make a great nation of his descendants through which the whole world will be blessed (Gen. 12:1-3). On his part Abraham had to leave the land of his youth and enter into the land promised to him. Abraham and his descendants also were required to circumcise all male descendants.
3. Mosaic Covenant: God established a covenant with Moses (Ex. 19-24) in which the Jewish people are freed from slavery and become God’s special possession. Not only will they be blessed but God will claim them as his very own. The Mosaic covenant has 613 commandments which the Jewish people must fulfill in order to receive the benefit of the covenant.
4. Davidic Covenant: God established a covenant with David that the messiah will come from David’s descendants (2 Sam. 7). This covenant did not task the Jewish people or Gentiles with any new commandments to fulfill.
5. The New Covenant: God promised to establish a new covenant through the prophet Jeremiah (Jer. 31:31-34) which was then fulfilled in Jesus (Luk. 22:20). This covenant does away with the legal requirements of commandments and replaces them with a desire of the heart to do the will of God. This covenant is with all humanity.