Many reasons have been offered for the reading of Megillas Rus on Shavuos. Here is one that I haven't seen anywhere: The Rambam at the end of Hilchos Chanukah teaches that the ENTIRE TORAH was given in order to bring peace to the world -דרכיה דרכי נועם וכל נתיבותיה שלום. The last mishna in Brachos learns from a passuk in Rus that there is a special mitzva to inquire about a friend's well being using Hashem's name "שואלים שלום חברו בשם". We learn from this megilla the importance of SHALOM. Shalom is so important that we can make use of Hashem's hallowed name in order to increase it. That is the purpose of the Torah!:)
May we be zoche to make peace between ourselves and others!!!