Here is an audio series covering the Covenants in scripture. It was given by Dr. Clifford McLain in 1986 near his retirement as pastor of Northside Bible Church. This audio series is one that covers the promises made by God throughout the ages as revealed in scripture. A good compliment to these audio lessons are the articles on Covenants as well as the large dispenational chart found in the Charts section.
The lesson on January 12, 1986 was part 1 of the "Convenants" study and is the first introduction to the series. The scripture reading in Jeremiah 31:31-37 KJV "31 Behold, the days come, saith the Lord, that I will make a new covenant with the house of Israel, and with the house of Judah: 32 Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the Lord: 33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the Lord, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. 34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the Lord: for they shall all know me, from the least of them unto the greatest of them, saith the Lord; for I will forgive their iniquity, and I will remember their sin no more. 35 Thus saith the Lord, which giveth the sun for a light by day, and the ordinances of the moon and of the stars for a light by night, which divideth the sea when the waves thereof roar; The Lord of hosts is his name: 36 If those ordinances depart from before me, saith the Lord, then the seed of Israel also shall cease from being a nation before me for ever. 37 Thus saith the Lord; If heaven above can be measured, and the foundations of the earth searched out beneath, I will also cast off all the seed of Israel for all that they have done, saith the Lord."