Hebrews 11:17-19 is the passage the New Testament builds on. It calls Isaac Abraham's one and only son, says Abraham reasoned that God could raise the dead, and says that in a sense he did receive Isaac back from death. The Greek word behind that phrase is parabole. The dominant reading takes the return as an enacted parable of resurrection. Adam Clarke offered a second in 1832, that parabole here means a jeoparding of life, so the verse describes an escape from imminent death rather than a figure. Both readings sit in the commentary tradition. Genesis 22:2 describes Isaac three ways in a row, your son, your only son, whom you love, and Romans 8:32 runs the same construction in reverse over God, who did not spare His own Son.
Genesis 22:6 puts the timber of a whole burnt offering on Isaac's back, and John 19:17 has Jesus carrying His own cross. Clement of Alexandria stated the reading about AD 200. Isaac was a son as the Son is, a victim as the Lord was, and all he did was carry the wood of his sacrifice. Origen worked it further about AD 245. Carrying the wood for a burnt offering is a priest's duty, so Isaac stands as victim and priest at once, and the text has him walking with his father rather than behind him. Bonaventure repeated the reading in 1257 and John Wesley in 1765. These are readings offered by named men, and Genesis makes no such claim about itself.
Genesis 22:13 says the ram was offered in place of his son. The Hebrew behind that phrase is tachath, and the same word carries the same load at Genesis 44:33, where Judah offers himself as a slave in place of the boy, to his father, over a brother. The vocabulary of Moriah comes back inside Isaac's own family two generations later. Isaac asked for a lamb and a ram came, so the lamb is still owed at the end of Genesis 22, and John 1:29 answers the question he asked. Two of the oldest Christian writers on the chapter set the limit that keeps the reading honest. Athanasius of Alexandria wrote in a festal letter about AD 334 that the death of Isaac would not buy freedom for the world, and that only the death of the Savior could. Caesarius of Arles said the same from the other side about AD 530, that the ram was killed and Isaac was not because Isaac was a figure and not the reality.
Hebrews 11:20 is the only verse in the Bible that credits Isaac himself with faith, and the chapter it credits him for is Genesis 27, where he was deceived. Matthew Henry, writing in 1710, put the weight where it belongs. Isaac's faith recovered itself and he ratified the blessing. Jesus then takes Isaac's name somewhere further. In Matthew 22:32 He builds the case for the resurrection out of a verb tense in Exodus 3:6, because God says I am the God of Isaac to Moses centuries after Isaac had died. He is not the God of the dead, but of the living. The son who was as good as dead and came back is named by Christ as proof that the dead live.
A second reading has a long history and no apostolic citation behind it. Genesis 24 has a father send a servant far off to bring a bride to the son, and Origen read Rebekah following the servant to Isaac as the church coming to Christ, about AD 245. Caesarius of Arles worked the same scene about AD 530. No New Testament writer applies Genesis 24 to Christ and the church, and the servant is never called the Spirit in Scripture. It is a reading held by named men, and this page presents it as a reading rather than as the meaning of the chapter.
Galatians 4:28 tells Gentile believers that they, like Isaac, are children of promise. Albert Barnes explained the mechanics with no triumph in them: born after the Spirit means born by the special agency of God rather than in the ordinary course of events. None of this takes anything from Israel. Romans 9 opens by insisting that God's word has not failed. Romans 11:1 asks whether God rejected His people and answers no. Romans 11:18 tells the grafted Gentile not to boast over the branches, because he does not support the root, the root supports him. Romans 11:29 says God's gifts and His call are irrevocable. Being a child of promise like Isaac describes how anyone comes in, by God's promise rather than by descent or by effort, and it takes nothing from anybody. This site's tradition holds that God's promises to Israel stand.