In the O.T. the Hebrew word for covenant is always b'rith. In the N.T. it is always diatheke . A covenant is a pact or agreement between two or more parties. God has initiated many agreements, or covenants, with different people throughout biblical history, i.e., Adam, Noah, and Abraham, etc.
Covenant is an important part of biblical history and, therefore, theology.
There is a flow to the covenants found in the Bible. Basically, it is as follows. First, God the Father made a covenant with the Son with regard to the elect. These additional covenants with people fall under the Covenant of Grace where God makes a covenant with the elect and promises them salvation through faith in Jesus. Some theologians say there is only one covenant, the covenant of redemption and that within this covenant are all the other covenants.