Why would you want to study a bunch of old, dead people?
Well, why do you read and study the Bible? Doesn't it tell you the story of a bunch of old, dead people? True, its central character, Jesus Christ, is still alive, but everyone else has long since passed away. But we desire to learn all we can know about Peter, Paul, James, John, and Priscilla. Why not others?
Hebrews 12:1 (NKJV)
1 Therefore we also, since we are surrounded by so great a cloud of witnesses, let us lay aside every weight, and the sin which so easily ensnares us, and let us run with endurance the race that is set before us,
There is this "great cloud of witnesses" watching us run our Christian race. Maybe, just maybe, if we look back upon the lives of some of these witnesses we can run a better race.
Christianity itself is deeply rooted in history. It involves two central groups of people - the Jewish nation and the body of Christ, the Church. The central figure of Christianity is Jesus Christ, God come to earth as a Man. The Person and Work of Jesus is a real-time historical event. The birth, sacrifice, burial, and resurrection of Jesus are historical events and form the cornerstone of your faith.
The entire story of the Bible is the unfolding of God's plan in history. The Gospel offers redemption for a hurting world. A study of church history is the study of God at work in the world carrying out His plan for mankind.
You are a member of God's church body. The history of the church is the story of your family. Studying the church over the ages helps the modern church understand controversies and heresies. Cults were present in A.D. 200. the same as they are present today. To understand Christian doctrine in its context of history helps us to separate fads and falsehoods from the truth of the Bible. The cults of today have already been dealt with in the distant past.
As a general comment, no two histories will view all events in the same fashion nor place emphasis in the same manner. What follows is a general survey of church history. Refer to the various sources, as well as many others that exist, for a more detailed study.
So, why study church history? Because it is the story of your family tree. All of these "great cloud of witnesses" are your distant brothers and sisters!