All Paul's epistles are gospel-centred, but in this one, which is relatively brief, he refers to the gospel frequently. Even though written from prison there is a dominant theme of joy that he wants the Philippians to share. But there is disunity in the church, and Paul addresses those people who have shown the genuineness of their faith (by a concern for the gospel), that they need to live worthily of the 'faith of the gospel'.
For The Sake of the Gospel - Philippians
Philippians simply explained
Mind, Body & Spirit