One final word of introduction. I always find the structure of literary works significant, especially when the author deliberately makes it that way. Calvin crafted this piece of literary art after the fashion of the Apostles' Creed, and hence, after the Trinity.
He begins with God the Father ("I believe in God the Father Almighty, Maker of heaven and earth..."), specifically as Creator, as Preserver, and finally as Governor of the universe. Book 2 continues with God the Son ("... and in Jesus Christ His only Son ..."), as Redeemer and as Mediator. Book 3 discusses God the Holy Spirit ("... I believe in the Holy Ghost ..."), as the bond of union between the believer and Christ. Finally, in Book 4, Calvin explores the "Holy Catholic Church," as the earthly means of applying the Gospel.
I find this beautiful. God, as Father, Son, and Holy Spirit is perfectly complete and self-sufficient in Himself. I might say that in a sense, Books 1-3 would form a complete, glorious, awe-inspiring unit, and the story could end there. God enjoyed unceasing, intimate, self-sacrificing fellowship in Himself. He has no need of anything or anyone outside Himself. Yet, in his perfect providence God wrote Book 4. He chose His Church to welcome into the very fellowship of the Trinity, which has existed from all eternity. We must thank God for Books 1-3, for revealing Himself to us. But, praise to His wonderful name for Book 4, for including us in His story!
But wait a minute! Calvin's "General Syllabus" talks plenty about man and redemption and salvation in Books 1-3. What's the big deal about the Church? I don't want to belabor the point right now. This is only the introduction. But I think we are going to see that without Book 4 we would be left with a very individualistic salvation. We would get the impression that the "church" was just a disparate collection of a bunch of individuals. We would get the impression that we could talk about soteriology without talking about ecclesiology. Calvin calls the activities of the Church ("the preaching of the Gospel and the use of the sacraments, with the administration of all discipline") means of bestowing faith. Thus, there is a gloriousness in the institution of the Church, and the story that it tells to the world. This, I think, is why Book 4 exists and what it is about.