Beurre blanc is a great classic of French cuisine: melt a knob of salted butter, whisk with the juice of a lemon and coat a poached slice of stingray or very simply some spaghetti cooked al dente.
Brown butter is butter cooked golden in a frying pan.
Black butter is brown butter to which capers have been added to color the butter so darkly that it appears black.
Clarified butter has been melted in a frying pan and cooled slightly, then strained through a chinois to eliminate the impurities. This operation allows for cooking butter without burning it. Clarified butter is widely used in India, where it is called ghee. Its origins date back 4000 years from the Levant. In Britanny, it was poured into clay pots and could be stored for two years, sometimes even longer.