I need to know from Christian

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On many discussion with Christian, I was told that the law in the Old Testment was not for the Christian or not apply to Christian. But when I looked in the Bible Matthew 5:17 - 20 "Think not that I come to destroy the law, or the prophets: I am not come to destroy but to fulfill. For Verily I say unto you, Till heaven and earth pass, one jot or one title shall in no wise pass from the law, till all be fullfilled. Whosoever therefore shall break one of this least commandments, and shall teach men so, he shall be called the least in the kingdom of heaven: but whosoever shall do and teach them, the same shall be called great in the kingdom of heaven. For I say unto you, That except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall no case enter into the kingdom of heaven." So my question is, which law is Jesus trying to fulfill ? If it is the law of Moses, why most Christian says it does not apply for them ? If it is not the law of Moses, then whose law is it ? Thanks for any explanation.