There may be special kinds you can eat. However, in general you are not advised to eat rinds of cheese like Edam.
Some cheeses, such as Babybel or Edam, are sealed with a wax. This should not be eaten. Also, some methods of cheesemaking form a rind on the outside of the cheese which is not especially tasty.
It's almost impossible to answer this because there are so many, and because different cheese makers may produce their own varieties. There are so many variables, such as type of milk, type of bacteria/rennet, how long it's aged, if it's got a washed rind, or a coating, or nothing at all. There are hard, soft, and semi soft cheese, as well as creamy styles. Wikipedia says there are currently 350 - 400 (or possibly up to 1000) distinct types of french cheese grouped into 8 main categories: fresh cheeses, soft cheeses with natural rind, soft cheeses with washed ring, pressed cheeses, pressed and cooked cheeses, goat cheese, blue cheese, and processed cheese.
There are a number of cheeses with a red rind, the best known being Edam and Leerdamer
Most Italian cheeses need to have their outer skin removed before being eaten eg hard pecorino cheeses. They are simply to protect the cheese inside during storage. It is advisable to do the same with gorgonzola even if it is softer.
Since there are over 300 cheeses made in France, this question has lots of answers! But if by TYPES you mean classifications: then here are several - Bloomy Rind, Washed Rind, Fresh, Blue-Veined, Double and Triple-Creme, Firm, Semi-Soft. If one considers simply the milk source...then you have Cow, Sheep and Goat's milk cheeses. Cheers from the Gourmet Cheese Detective!
Usually, Kumquats are eaten with their rinds since their center is sour and the rinds are sweet.
As a proper noun, Rine is a word. However, rine (small case) is an obsolete word for rind. Rind is the thick, outer covering of certain fruits, meats and cheeses. Examples include: orange rind, watermelon rind and bacon rind. Rind is also the bark of a tree.
Tomme is the most common soft Swiss cheese. Brie-type soft cheeses are also made in Switzerland.
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Brie /ˈbriː/ is a soft cow's cheese named after Brie, the French region from which it originated (roughly corresponding to the modern département of Seine-et-Marne). It is pale in color with a slight grayish tinge under a rind of white mold; very soft and savory with a hint of ammonia. The whitish moldy rind is typically eaten, the flavor quality of which depends largely upon the ingredients used and its manufacturing environment
Soft cheeses that require refrigeration such as ricotta.
In China, the rind of a watermelon is fried and eaten. They also use the watermelon seeds as a snack (eaten like sunflower seeds.)