In this shiur we dealt with the famous debate of Beit Shammai and Beit Hillel regarding the nature of the appropriate hidur for the lighting of the candles. We showed how the debate of Tosafot and Rambam can be read into the berayta itself. We then noted the unique situation in which the Rema paskens like the Rambam and the Mechaber paskens like Tosafot (Taz there).
The comments of the Beit haLevi begin the process of moving away from the miracle of the oil as the central event of the Holiday.
Here are the mekorot that worked with in shiur (link).