ANSWER: Covenants are an "agreement between two parties containing their promises each to the other" according to Webster's Dictionary. There are many of them in the Bible between men and between nations that are not listed here. There are also covenants that are not designated as such in the scripture where the agreement is reached, i.e., God's covenant with Adam and Eve in the Garden of Eden concerning what fruit they could eat and what fruit they could not eat.
Below are some of the covenants made by God that are in the Bible.
God made a covenant with Noah to save him and his family (Genesis 6:18). He also promised him and his descendants to never again destroy the world by flood (Genesis 9:9-17).
An agreement was made with Abram (Abraham) to give him and his descendants the land we call Israel and to destroy its then current inhabitants because of their great sins (Genesis 15:18-21).
God made an unconditional covenant with Abram, whereby he changed his name to Abraham and designating him the father of many nations and millions of descendants. Abraham's and his descendants part of the agreement was to have all their males circumcised (Genesis 17).
A conditional agreement was made with the children of Israel, requiring their keeping God's law and circumcision, in return for physical blessings. (Exodus 19 - 24). Further terms (conditions) of this covenant were expounded later. (Leviticus chapters 25 - 27; Deuteronomy chapters 29 - 31)
A covenant was made with the Israelites regarding the Sabbath (Exodus 31:14 - 18), the commandments and God's Feast days (Exodus 34:10 - 35).
An unconditional covenant was made with King David of Israel and with Jacob's descendants. (Jeremiah 33:19-36).
The most important covenant, the NEW covenant, was established by Jesus upon His death. (Jeremiah 31:31 - 34, Matthew 26:28; Mark 14:24; Luke 22:20; 2Corinthians 3:6; Hebrews chapters 7 - 10). Paul described the only new ritual of it (1Corinthians 11:23 - 30).
The word "testament" is interchangeable with "covenants." The King James Version Bible sometimes translates the Greek word diatheke as "testament" and sometimes as "covenant." Many other Bible translations use "covenant" exclusively. We could just as easily refer to the two common divisions of scripture as the "Old Covenant" (since it contains descriptions, prophecies and books of wisdom from people living under it) and the "New Covenant" (containing the story of Jesus and people who lived during the transition from the old to the new one).