What is an overview of the differences between Old Testament and New Testament? I am a Muslim and I am trying to understand the Bible for educational purposes. 

I've never known anything about the Bible apart from the fact that it exists. Now I have heard in many debates and Christian speeches of verses from The Old Testament and verses from The New Testament. 

My question is simple, what is an overview of the differences between the Old and New Testaments? Are they still a part of the Bible?

Keep in mind I know nothing about Christianity so excuse me if my question doesn't make sense.
The Old Testament consists of books written by the Jews during the centuries before Jesus was born. It is believed to contain the entire history of the Jews all the way back to the creation of the world. The Old Testament is important to Christians because it is thought to include prophecies of Jesus.

The New Testament consists of additional books written by Christian authors, but not accepted by Jews as scripture. Four of these books, known as gospels, contain an account of the life of Jesus and another book, known as Acts of the Apostles, is believed to be a history of the early Church. Other books are letters, or epistles, believed to have been written by Christian apostles.

The Bible consists of both the Old Testament and the New Testament, following in that order.  When discussing Judaism, Christians sometimes refer to the Old Testament as the Hebrew Bible, but Jews would call it the Tanakh.