What does the Gospel Of Paul teach us that is different from the other Gospels?

I think you have seriously confused yourself with the
various books of the Bible. There is no actual "Gospel of Paul." There are only four
gospels in the New Testament, Matthew, Mark, Luke and John. However, Paul is definitely
the most prolific writer of the books we have that make up the New Testament. He is
responsible for a series of letters or "Epistles" to various church groups. These are
mostly called after the area that they are sent to or the area in which they were
written, such as Romans, Corinthians and Ephesians. Key to note in terms of the
difference between the Pauline Epistles and the Gospels is the way that Paul's writings
focus on the development and challenges of the early church as it seeks to work out how
to respond to the call to follow Jesus Christ and his teachings in the context of the
time. Thus we have teaching regarding issues such as the circumcision of Gentiles,
response to authorities and rulers, legalism and Jewish customs for the Gentile
believers and how Christians should respond in the face of persecution. The main focus
of the Gospels is obviously the life and times of Jesus and his teaching. The Pauline
Epistles seek to explore how that is applied into the context of the early
church.