Exodus 32-34

Moses was up on the Mountain for 40 days (Exodus 24:18). At some point during that stretch, the people grew weary of waiting and asked Aaron if he would make them a god or gods. Aaron commanded them to bring their jewelry to him, with which he fashioned a golden calf for them to worship. It's difficult to discern here, if they were breaking the 1st or 2nd Commandment (or both). Were they worshiping a different god or were they trying to worship the true God through and image they could see? Whatever the case, their actions cannot be justified. Their compromise on 'worship' led to a compromise in 'morality' and they indulged in revelry after making offerings to the golden calf (32:6).

Moses is, of course, oblivious to all of this while up on the mountain until the Lord informs him of those circumstances. God calls them "your people" (Moses' people). He calls them a stiff-necked people. He tells Moses to leave Him alone so that He can destroy Israel and start over with just Moses. Was this really God's intention or was he motivating Moses to pray? I think the latter since Moses then disobeys the command to be left alone and the prayer is answered. This is the 1st of 4 interesting prayers in this section of Exodus:

Prayer #1
Don't destroy Israel
a. They are YOUR people
b. It's YOUR reputation as stake
c. It's YOUR promise that they'll flourish

God relented in response to Moses' prayer. Moses then went down the mountain, meeting a very patient Joshua along the way. But as they approached the camp they heard the wild party going on below. Joshua thought it was the sound of war, but Moses recognized it as singing. When he saw the dancing and the calf, he became very angry and threw the 10 commandments to the ground. They were shattered. He burned the calf in the fire, scattered it in the water, and made the Israelites drink it. He then questioned Aaron regarding how this had come about. Perhaps he imagined that the Israelites had tortured him into compromising the faith. Unfortunately for Aaron, all that was required for him to compromise was the people asking aggressively. Aaron also lied by claiming that the golden calf had, basically, made itself. Moses recognized the leadership failings of Aaron. He called for all those who were for the Lord to come to his side. Only the Levites came. They were commanded to punish the evil-doers with the sword. 3000 were killed (1 Corinthians 10:8 records the number as 23,000, but this may be the total number killed by sword and plague).

Prayer #2
Forgive Israel of her sins
Moses asks God to forgive Israel or blot his own name out of 'the book' (presumably the book of life). But God responds by declaring that sinners alone will be blotted out. In essence, God says "No" to this prayer request. Only Jesus can atone for sin, Moses has no such power.

The people were punished via plague before re-starting their journey toward the Promised Land. But this time God threatens to not go with them (He states that if He were to go with them, He might get angry and destroy them along the way). He will, instead, send an angel with them. But when Moses and the people heard this threat, they begged for God's presence along their path.

Prayer #3
Moses asks for God's help
a. We don't want to go without your presence
b. We are distinguished by your presence
Response: God agrees to go with Israel

Once again, I don't think God really wanted to NOT go with His people. He wanted them to recognize the necessity of His presence. And, in this case, they did so. The prayer request was granted. Moses takes this "Yes" as a motivation to ask for one more thing:

Prayer #4
Moses asks to see God's glory
But God declares that no one can see His glory directly and live. And so Moses is allowed only to see the backside of God's glory (the glow that remains after). Moses is confronted, in this encounter, with God's nature:

1. Compassion
2. Grace
3. Patience
4. Deep Love
5. Faithfulness
6. Wide Love
7. Forgiveness
8. Justice

Moses is awed by this encounter and, once again, begs God's guidance for their journey. God responds by declaring His covenant with Moses and Israel. He will do wonders and defeat their enemies. They, in turn, are not to make treaties with those people groups. They are to break down the religious infrastructure of their enemies because God is a jealous God. They are reminded of the dangers of inter-faith marriage and the importance of celebrating holy days. This encounter b/w God and Moses lasted another 40 days (34:28).

When Moses came down the mountain, again, after these 40 days, 'his face was radiant because he had spoken with the LORD.' The people were afraid. Moses ended up putting a veil over his face afterward whenever he came from the presence of the LORD. Paul discusses these things in 2 Corinthians 3:7-18.