What was the purpose of Paul's letter to the Galatians?

The purpose was to prove to the Gentile believers in Galatia that they were not under the Mosaic Law but under grace. Paul wrote to correct their desire to return to the weak and beggarly elements of the Law, showing why a believer who has tasted grace should not go back into bondage.

Les explains that the whole thrust of this little book of Galatians was to prove to these Gentile believers up in Galatia that they were not under the Mosaic Law, they were under grace. He notes that the Law was weak and beggarly, yet they thought they wanted to go back under it. Paul strongly opposed this, saying he could raise his voice against them, because it was a horror that a believer would want to return to the Law after tasting grace. Les contrasts this with Romans 8, where the righteousness of the Law is fulfilled in believers who have that position in Christ by believing the Gospel.

Galatians 4:8

Howbeit then, when ye knew not God, ye did service unto them which by nature are no gods.

What was the whole point of the book of Galatians?

The whole point of Galatians was to prove to Gentile believers in Galatia that they were not under the Mosaic Law but under grace. Paul argued the Law was weak and beggarly, and he was astonished that believers who had tasted grace would want to return to bondage under the Law.