How did Moses serve Israel in the passage Peter quotes in Acts 3?

Moses served Israel as the Deliverer and Redeemer, bringing them out of slavery and leading them out of captivity to Abraham's God. In the passage Peter quotes, Moses is a type of the coming Deliverer, and Peter applies that role to Israel's need for repentance and belief.

Les teaches that in Acts 3, as Peter speaks to the great crowd of Jews, he takes them back to Moses' role in Israel's life. Moses was the deliverer and, in so many words, the redeemer: he brought them out of slavery, led them out of captivity, and brought them to Abraham's God. Peter then uses Moses as a type of the Deliverer to come. Les points out Peter is still on covenant ground, and the passage leads to the call in verse 23: if Israel would repent, no unbelieving Jews would enter, and the admonition is for every Jew to become a believer, because no unbeliever will enter the Kingdom of Heaven.

Acts 3:22

For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you.

In what way was Moses a type of the Deliverer and Redeemer?

Moses served as a type of the Deliverer and Redeemer by bringing Israel out of slavery, leading them out of captivity, and bringing them to Abraham's God. Even as Moses was the Deliverer in type back then, Peter continues on covenant ground, calling every Jew to become a believer and be born again.