Sometimes known as the dispensation of "Promise;" this is where God makes many promises to his people and makes a covenant with Abraham (God changed his name from Abram) which was wholly gracious and unconditional.
The descendants of Abraham had to simply abide in their own land to inherit every blessing. They lost those blessings in Egypt; but not their covenant.

The dispensation extends from Genesis 12 through Exodus 19. Exodus is where the Jews were led from bondage out of Egypt by Moses. The dispensation of Promise ended when Israel rashly accepted the law in Exodus 19:8. Grace had prepared a deliverer in Moses, provided a sacrifice for the guilty, and by divine power brought them out of bondage; but at Sinai they exchanged grace for law.

As in all the dispensations; God tests man, and they end in a judgement. However, we must understand that the Covenant and the dispensation must be separated. The dispensation is a way of testing, or a certain way in which God deals with man. The covenant, is everlasting, as it is unconditional and a promise made by God.

The "law" did not negate the Abrahamic Covenant

"Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many;but as of one. And to thy seed, which is Christ. And this I say, that the covenant , that was confirmed before of God in Christ , the law, which was 430 years after, connot disannul, that it should make the promise of none effect. For if the inheritance be of the law, it is no more of promise; but God gave it to Abraham by promise." Galatians 3:16-18

it was simply an "intermediate disciplinary" dealing "until the Seed should come to whom the promise was made." Only the dispensation ended with the giving of the law - the promise by God, still stood. For a summary of the Abrahamic Covenant see Genesis 15

Other Dispensations

Man Innocent - The First Dispensation

Man Under Conscience - The Second Dispensation

Human Governmant - The Third Dispensation