These are the specific promises God made to Abraham in a condensed form.
Promises: Make of him a great nation, Bless him, make his name great, he would be a blessing and all familiies of the earth would be blessed in him
Genesis 12:1-3 Now the LORD had said unto Abram, Get thee out of thy country, and from thy kindred, and from thy father's house, unto a land that I will shew thee: 2 And I will make of thee a great nation, and I will bless thee, and make thy name great; and thou shalt be a blessing: 3 And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed.
Promises: All the land thou seest, will be given to thee and to thy seed forever
Genesis 13:14-17 And the LORD said unto Abram, after that Lot was separated from him, Lift up now thine eyes, and look from the place where thou art northward, and southward, and eastward, and westward: 15 For all the land which thou seest, to thee will I give it, and to thy seed for ever. 16 And I will make thy seed as the dust of the earth: so that if a man can number the dust of the earth, then shall thy seed also be numbered. 17 Arise, walk through the land in the length of it and in the breadth of it; for I will give it unto thee.
Promise: Give thee the land from the Nile to the Euphrates
Genesis 15:18-21 In the same day the LORD made a covenant with Abram, saying, Unto thy seed have I given this land, from the river of Egypt unto the great river, the river Euphrates:
19 The Kenites, and the Kenizzites, and the Kadmonites,
20 And the Hittites, and the Perizzites, and the Rephaims,
21 And the Amorites, and the Canaanites, and the Girgashites, and the Jebusites.
Promises: Be a God unto thee and to thy seed, Land of Canaan forever for an everlasting possession, Sarah will bear a son, Establish covenant with him and his seed for an everlasting covenant
Genesis 17:7-8 And I will establish my covenant between me and thee and thy seed after thee in their generations for an everlasting covenant, to be a God unto thee, and to thy seed after thee.
8 And I will give unto thee, and to thy seed after thee, the land wherein thou art a stranger, all the land of Canaan, for an everlasting possession; and I will be their God.
Promises: Multiply thy seed, seed will possess the gate of their enemies, Thy seed, all nations of the earth blessed
Gen 22:17-18 That in blessing I will bless thee, and in multiplying I will multiply thy seed as the stars of the heaven, and as the sand which is upon the sea shore; and thy seed shall possess the gate of his enemies;
18 And in thy seed shall all the nations of the earth be blessed; because thou hast obeyed my voice.
In addition to the clearly stated promises, God has Inferred promises to Abraham: Since Abraham died without inheriting the promises, God infers resurrection back to life for Abraham. Since no one can inherit anything forever because we all die, God's promise that God would give him the land forever infers that he will be given eternal life.
"...in thy seed shall all the nations of the earth be blessed..." and "...seed shall possess the gate of his enemies..." infers a great king to come who, by the grace of God, will save all mankind from eternal death and provide the one path to bring man out of the grave unto eternal life. This man's name was Jesus Christ.
The fact that these promises are still relevant today is attested to by Galatians 3:28, where being baptized into the name of Christ makes us heir to these promises and the hope they convey for resurrection to life again
Galatians 3:26 For ye are all the children of God by faith in Christ Jesus. 27 For as many of you as have been baptized into Christ have put on Christ. 28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. 29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
These promises are the central theme of all scripture and the hope of life to all mankind. These promises are mentioned all throughtout scripture, showing that it was the hope of the prophets and faithful servants of God from time immemorial. Take some time to study these promises and understand them, and you will suddenly notice them all throughout scripture.