Is the Old Testament a Jewish religous book and should it be discarded by Christians today? If not what does it add to Christians today?
The opening to the book of Hebrews sheds some light on this:
This affirms that long ago (well before the time of the New Testament), God was speaking to mankind. As Jesus pointed out in Luke 6:45, "out of the overflow of the heart the mouth speaks," so spoken words reveal the heart of the speaker. In the same way, the spoken words of God reveal God's heart as well. So, the Old Testament reveals the heart of God in many ways.
Paul also mentions the benefit of the Old Testament, stating that hope can come through the Scriptures--and at the time he wrote Romans, there wasn't much Scripture outside of the Old Testament.
Luke also notes that the people of Berea were considered noble for the very fact that they studied the Old Testament.
These people searched the Old Testament Scriptures and concluded that Paul's messages was, indeed, true and that Jesus was, indeed, the Messiah. This verification is very important today, as the Old Testament continues to show that God had prepared the world for the coming of the Messiah, and that the Son of God became a Man named Jesus who was that Messiah.
Jesus Himself noted that the Old Testament Scriptures actually spoke and testified about Him:
Finally, the Old Testament was not written just for Jews. In the lineage of Jesus Himself, there is mention of a Hittite (Urriah), a Moabite (Ruth), and a woman of Jericho (Rahab). The promise to Abraham was that he would be a blessing to all people--not just his own descendants through Isaac.
Even in Egypt, the purpose of the plagues was to show the Egyptians that the God of Israel was the one true God.
The Egyptians shall know that I am the LORD, when I stretch out my hand against Egypt and bring out the people of Israel from among them. Exodus 7:5 ESV
Also, Genesis is believed by many to have been a collection of writings from Adam, Noah, and others. If so, Adam and Noah were not "Jewish", but the ancestors of all people alive today.
So, the Old Testament can be considered a Jewish book, written by Jews (with the possible exception of Genesis) under the inspiration of God, to proclaim God's name to all mankind.
It should also be noted that the New Testament is written entirely by Jews as well. In fact, Christianity is inherently Jewish and was begun by all Jews. It could easily be described as Gentiles (as well as Jews) recognizing Jesus as the promised Jewish Messiah of the Old Testament.
Lastly, Paul's letter to Timothy emphasizes that all Scripture is of value. At the time of his writing, he certainly intended to include the Old Testament.
Both the Old and New Testaments are the revelation of God, and, as such, are the primary means by which we can know God Himself.
You are asking two completely separate questions.
1. Is the Old Testament a Jewish book?
Insofar as the Torah was revealed first to the Jews, yes. As Romans 9 points out
But, is the promise made to Jews alone? Paul continues:
Whether or not we are descended from Abraham (or even Isaac) here is irrelevant - Paul admits it is not the children by physical descent who are God's children. Whilest I am always a little bit leery of putting the church in the place of the Jews in all things, it is fair to say that we are heirs of the same promise.
2. Should it be discarded?
Jesus himself said in the Sermon on the Mount (Matt 5:17)
Futhermore, Paul - the biggest opponent of "the law" if there ever was one - even he says (Galatians 3:17):
He goes on to call the law a "pedagogica" - think of it as a nanny - that leads us to Christ. It is the thing that makes us aware of our sin
In Romans 7, he makes the same point:
In all these things, the OT law still has a purpose - it makes us aware of our need for God.
Frankly, it also tells us who God is.
So, in short, no, we can't discard the OT - it's the foundation without which grace makes no sense.
The books of the old Testament were written by Jews for Jews, so yes, it's a Jewish book.
It's also the history of the chosen People of God to whom the redeemer Jesus Christ was promised, who fulfilled the law and the prophets and guided the People of God into the new testament as Christians. So it's our book too as Christianity is the continuation of Israel, the true People of God here on earth.
First the Old Testement isn't 'one' book its lots of books. Second many of the books that are in the current version the Old Testament are in the Jewish religious book the Torah. So it is technically 'a Jewish book' Third, The New Testament was in fact written by Jews. God had to command Peter to take the gospel to others because they were Non Jewish.
As for what it adds today it is very appropriate for depicting good and bad behavior in the gospel. Also there are many prophecies in the Old Testament that have not been fulfilled... Which means if for nothing else there are still things we can learn about the Second Coming from the Old Testament.