A Gentile is not required to keep the 613 Laws of the Torah. The Seven Noachide Laws are the gentiles guidelines for life. They are:

Prohibition against idol worship
Prohibition against blasphemy
Prohibition against murder
Prohibition against adultery
Prohibition against theft
Prohibition against eating flesh from a living animal
Establishing courts of justice

If a Gentile fully keeps these seven laws he is considered as righteous as the High Priest of Israel.   But what if he desires to observe more?  Is he permitted to do so? 

The Torah being read at Sukkot (a feast for all nations)

The Noachide Oath, administered by rabbis of the Sanhedrin in Jerusalem ... Click Here for more information