Did Jesus ever say in the Bible to preach Christianity or his message to the Non-Jews? My question is very simple: did Jesus mention or command his followers to go and preach Christianity (worshiping Him) to Indians or the Non-Jews? If he did not mention it why are Christians preaching around the world? Does this mean that Jesus's message was only for a particular group of people and not for the whole of humanity? Please  be specific.
Yes.  While Jesus did tell his followers to focus on the Jews and not the Gentiles during his lifetime, after the Resurrection that changed, quite explicitly:


  And he said unto them, Go ye into all the world, and preach the gospel to every creature.
  
  --Mark 16:15


Matthew records a slightly different version of this commission:


  Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost
  
  --Matthew 28:19


The wording differs between the two passages, but both quite clearly mention the universal nature of the charge to teach the Gospel.