Hastings' Dictionary of the New Testament 
LEVI. — 1. The name occurs twice in our Lord’s genealogy ( Luke 3:24; Luke 3:29). 2. See Levites and Priest. 3. See Matthew.
International Standard Bible Encyclopedia 
( לוי , lēwı̄ ; Λευεί , Leueı́ ): The third of Leah's sons born to Jacob in Paddan-aram ( Genesis 29:34 ). In this passage the name is connected with the verb lāwāh , "to adhere," or "be joined to," Leah expressing assurance that with the birth of this third son, her husband might be drawn closer to her in the bonds of conjugal affection. There is a play upon the name in Numbers 18:2 , Numbers 18:4 , where direction is given that the tribe of Levi be "joined unto" Aaron in the ministries of the sanctuary. The etymology here suggested is simple and reasonable. The grounds on which some modern scholars reject it are purely conjectural. It is asserted, e.g., that the name is adjectival, not nominal, describing one who attaches himself; and this is used to support theory that the Levites were those who joined the Semitic people when they left Egypt to return to Palestine, who therefore were probably Egyptians. Others think it may be a gentilic form lē'āh , "wild cow" (Wellhausen, Prolegomena , 146; Stade, Geschichte des Volkes Israel , 152); and this is held to be the more probable, as pointing to early totem worship!
Levi shared with Simeon the infamy incurred at Shechem by the treacherous slaughter of the Shechemites ( Genesis 34 ). Jacob's displeasure was expressed at the time ( Genesis 34:3 ), and the memory was still bitter to him in his last days ( Genesis 49:5 f). The fate predicted for the descendants of Simeon and Levi ( Genesis 49:7 ), in the case of the latter on account of the tribe's stedfast loyalty in a period of stern testing, was changed to a blessing ( Exodus 32:26 ). In later literature the action condemned by Jacob is mentioned with approval (Judith 9:2 ff). Levi was involved in his brothers' guilt with regard to Joseph (Gen 37), and shared their experiences in Egypt before Joseph made himself known (Gen 42 through 45). Three sons, Gershon, Kohath, and Merari, were born to him in Canaan, and went down with the caravan to Egypt ( Genesis 46:11 ). Nothing further is known of the personal history of this patriarch. He died and found sepulture in Egypt. For the tribal history and possessions, see Priests And Levites .