Exodus 32 is one of the saddest chapters in Israel's history. While God is giving Moses the tablets and the plans for His dwelling, the people are breaking the covenant at the foot of the mountain. Impatient at Moses' delay, they demand gods which shall go before us. Aaron fashions a golden calf and declares a feast to Yahweh (32:5). They tried to worship the true God through an image, which God had forbidden only weeks before (20:4-5).
God tells Moses that the people are stiff-necked and that He will consume them and make a great nation from Moses. Moses intercedes, appealing to God's reputation among the Egyptians and to His covenant promises to Abraham, Isaac and Israel. So Yahweh turned away from the evil which he said he would do to his people (32:14). Scripture uses human language to show that God truly responds to prayer, while His purposes do not fail (Numbers 23:19).
Moses breaks the tablets, a vivid sign that the covenant has been broken, and destroys the calf. Aaron makes excuses, even claiming the calf just came out of the fire (32:24). The Levites side with Moses, and judgment falls on about three thousand people; a plague follows. This passage is hard to read, and it shows the seriousness of idolatry. Then Moses offers himself: Yet now, if you will, forgive their sin—and if not, please blot me out of your book which you have written. God says each person is responsible for their own sin. Moses could not take the people's place. In the New Testament, 2 Corinthians 5:21 says Jesus, who knew no sin, was made sin for us.