It would be good to have a basic knowledge of other people on this earth to better understand them.  So we will cover the basic tenets of those religions so there is better understanding.

Christianity is made up of 3 major sects: Protestant, Roman Catholic, and Eastern Orthodox.  Amongst Protestant there are many denominations such as Lutheran, Baptist, Pentecostal, Episcopalian, Methodist, etc…And in Eastern Orthodox there are many denominations such as Greek, Russian, Serbian, Ethiopian, Coptic (Egyptian), etc…  In mainstream Christianity (these 3 sects), the basic tenets are that God is a triune God that is made up of a Father, Son (Jesus), and Holy Spirit (ghost).  They call Jesus the Word of God and they believe that the Word was God and the Word was made flesh.   So that God became incarnate in the body of Jesus, similar to the Hindu belief in Avatars (God become flesh).  Hindus as well have a trinity (Brahman, Vishnu, and Shiva), and that God became flesh in Krishna.  A good book to read on this subject “the book your church does not want you to read.” 

They believe that according to the Old Testament in the ancient Temple of Solomon in Jerusalem that to remove sins, it required blood sacrifice (of sheep, goats, cows).  And so they believe that since Adam brought sin and death into the world with the original sin, that there was needed a savior (a Messiah) that could redeem them from this original sin, and save the world through his sacrificial blood (Hebrews 13:20).  Now according to the O.T. it was required that the sacrifice be perfect, without blemish, and the Christians believe the only way that is possible is if the sacrifice is indeed God seeing as though all normal men are full of sin.  And thusly the belief that God the father sacrificed his son Jesus, to absolve humanity of their original sin of disobeying God by eating from the tree of knowledge in the Garden of Eden.  And this blood atonement of him going to the cross absolves humanity of their sin, if they believe in him.

The problem though with this thesis is that according to Judaism, because the Temple does not stand anymore God just wants us to repent of our sins and then God will forgive us of our sins.  God does not NEED blood sacrifice to atone for sins as the Prophet Hosea says in 6:6, "For I desired mercy, and not sacrifice; and the knowledge of God more than burnt offerings."  Besides that, the thought of a human sacrifice is a totally pagan idea.  God totally forbids human sacrifice, and thusly the whole theology of Jesus being a blood sacrifice is actually blasphemous!  Christians actually say that through the "Blood of the Lamb, your sins are forgiven."  Referring of course to Jesus as the Lamb of God, because Lambs used to be sacrificed in the Temple in Jerusalem.

And so the majority opinion is that for someone to be saved and go to Heaven, they need to accept that Jesus died on the cross for their sins and was resurrected the “3rd Day”.  Even in the Bible (Corinthians), it says that if Jesus did not rise from the Dead, then indeed the whole Christian faith is in vain.  And that is why Christians have historically hated Muslims, and labeled us infidels, in that by denying the crucifixion, we are in fact denying the whole Christian faith, regardless that we believe in the virgin birth, his Prophethood, and him being the Messiah. 

Another interesting note is that in the Bible it teaches that one who has good faith will produce good works (deeds).  So the misconception that most Muslims and even Christians have is that if they believe in Jesus and still do evil, they will still be saved.  In fact the Bible teaches that if in fact the person does evil deeds, they don’t truly have real faith, and thusly won’t be saved. Theological beliefs are simply not enough for the gentile to
stand righteously before G-d. Even the Christian Bible acknowledges this.
James says, "faith without works is dead" (C.B. James 2:17,20). Jesus says in the Gospel, “You will know a tree by its fruit.”  So if the tree (Christian) bears bad fruit (doing evil) then in fact he does not really have faith, and will thusly not be saved.  Just as a Muslim who professes the Shahadah, but then goes and kills innocent people (women, children, civilians), he is not promised Paradise.  If you really believe in Islam, you are going to follow its laws (Shariah), and not just follow your own ideologies (political or nationalistic, etc.). 

The reason that Christians have a basis for believing in Jesus’ divinity is mainly the Gospel of John and the writing of Paul (which make up the majority of the New Testament).   What is interesting is that the order in which the Gospels were written were Matt, Mark, Luke, and John.  So the fact that the last one to be written is John’s Gospel, it thusly is the least one to be trusted as accurate.   Just as if something is written as an eye witness account and another account was written 100 years after the event, which account are you going to trust?  When the N.T. was canonized, there were many Gospels that did not even believe that Jesus was crucified nor that he was divine, and those did not make it into the Bible, such as the Gospel of Barnabas.  Now I am not saying that the Gospel of Barnabas is totally accurate either, because it is not.  An example of this is that that Gospel claims that Muhammad (Saws) is the Messiah.  Whereas we know from the Qur’an and Hadith that in fact Jesus is the Messiah and that he will return to kill the Dajjal.  Whereas our Prophet died a natural death and will not return to kill the Dajjal. 

Another thing is that Paul never met Jesus either.  He supposedly had a mystical vision of him on the road to Damascus, where Jesus commissioned him, and received “divine inspiration” but he never met Jesus and never received revelation.  He is the main one to promote the ideas of Crucifixion for the sins of mankind and that Jesus is the divine son of God.  These were not the actual teachings of Jesus, except for some untrustworthy statements in John, which Biblical scholars admit are latter additions to the original.  In fact what most Christians read are translations of translations.  Jesus and his disciples would of spoke Aramaic and Hebrew.  But what the English Translations of the NT translate from is a Greek version of the NT, that is the oldest copy of the NT they have.  They don’t have the original Aramaic Gospels, except maybe in the Vatican in Rome, which no one but the Pope and his Cardinals see.  For example King James Version written in 1611 is a translation of the Greek. 
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Now the issue of Judaism.  It should be noted that out of 15 million Jews, only about 2 or 3 million are Traditional Orthodox. The majority of the rest are just secular/liberal (reform, conservative, reconstructionist).  It also should be noted that Judaism (Torah and Prophets) and Zionism (Jewish Nationalism or  Atheistic Socialism) are two different things.  Just as Islam (Qur’an and Sunnah) and Palestinian or Arab Nationalism (PLO, Hamas, etc.) are two totally different entities.  But if we compare the fundamental beliefs (aqeedah) of the two religions, they are fundamentally the same. (The seven articles of faith in Islam and 13 in Judaism). 

1. The belief in the oneness (Tawheed) of Allah
2. To believe in all of his Prophets (that indeed God does communicate to humanity through Prophets).
3. To believe in all of his Angels.
4. To believe in all of his books.
5. To believe in the Last Day and the resurrection of the Dead
6. To believe in Heaven and Hell.
7. To believe in Qadar

The main differences relate to:
1) Shariah. For example some of the Dietary laws (such as camel and shellfish (except Hanafi), and the Sabbath and the holidays such as Rosh Hashanah and Yom Kippur. 

2) Jews believe that the covenant (Torah) that God made with Bani Israel is an eternal or everlasting covenant (see Genesis 17 and 28; Exodus 6 and 31; and Leviticus 26; and Deuteronomy 4; and Psalm 105; Jeremiah 32; Ezekiel 16 and 37). That just because they did not accept Jesus as their Messiah, they were not rejected by God.  And that the Torah is to be followed by Bani Israel till the Day of Judgment.  Jews also believe that there are two covenants for humanity.  That non Jews have to follow the 7 laws of Noah, and if they do so, then they will enter Paradise as righteous Gentiles.  (An explanation of the the 7 laws of Noah can be read at http://www.chabad.org/library/article.asp?AID=42592 )That is why Jews have traditionally discouraged conversion, because it makes it that much harder for people to enter Paradise.  For a Jew to go to heaven, they must follow the 613 laws of the Torah.  Whereas a Non-Jew only has to follow the 7 laws to go to heaven.  Now remember that most non-Orthodox Jews are totally ignorant of their religion, and they probably don’t know this, if you were to talk to the majority of Jews. 

3) The other difference is the issue of Prophecy of the future.  For example, the Torah had already Prophesized that if the Jews do not follow the Torah they would be exiled to the four corners of the earth.  But that in the end of days, before the Day of Judgment, they would be gathered out of various nations and back into the Biblical Land of Israel. 

Qur’an 17:104; PICKTHAL: “And We said unto the Children of Israel after him: Dwell in the land; but when the promise of the Hereafter cometh to pass We shall bring you as a crowd gathered out of various nations.”

Qur’an 5:20-21; YUSUF ALI: “Remember Moses said to his people: "O my people! Call in remembrance the favor of Allah unto you, when He produced prophets among you, made you kings, and gave you what He had not given to any other among the peoples.  "O my people! Enter the holy land which Allah hath assigned unto you, and turn not back ignominiously, for then will ye be overthrown, to your own ruin."

Qur’an 7:137; YUSUF ALI: “And We made a people, considered weak (and of no account), inheritors of lands in both east and west, - lands whereon We sent down Our blessings. The fair promise of thy Lord was fulfilled for the Children of Israel, because they had patience and constancy, and We leveled to the ground the great works and fine buildings which Pharaoh and his people erected (with such pride).”

I think it would be important for Muslims to read the Torah, especially Deuteronomy, chapters 28-32.  If you don’t have a Bible at home, I would recommend http://www.blueletterbible.org/kjv/Deu/Deu028.html   It is important for Muslims to know what other people of faith believe, especially the Ahl Kitab (the previous Muslim Ummah).  What it talks about in these 5 chapters covers many of the issues (Prophecies fulfilled) that we encountered in the 20th century.  More information about this can be reviewed on my website http://binsalaam.tripod.com
It is really important to note that if the Qur’an and Hadith do not contradict something that is in the Torah (Taurat) of Prophet Musa  or the Psalms (Zabur) of Prophet Dawood, then we have absolutely no reason to reject it just because it does not fit with our own personal political ideology.  The only reason we would have to say that that verse was not in the original Torah, is if the Qur’an or Sahih Hadith tells us something differently.  Remember that Prophet Muhammad (saws) did not come with a different and new religion, he came with the same religion of Musa, Dawood, and Isa. 

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YUSUFALI: “And this was the legacy that Abraham left to his sons, and so did Jacob; "Oh my sons! Allah hath chosen the Faith for you; then die not except in the Faith of Islam (Submission to God)."

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YUSUFALI: “The same religion has He established for you as that which He enjoined on Noah - the which We have sent by inspiration to thee - and that which We enjoined on Abraham, Moses, and Jesus: Namely, that ye should remain steadfast in religion, and make no divisions therein: to those who worship other things than Allah, hard is the (way) to which thou callest them. Allah chooses to Himself those whom He pleases, and guides to Himself those who turn (to Him).”

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