In lecture (which we have after kitchen work), we've also learned a lot about eggs - their different purposes, different sizes/grades, different market forms, and the different ways of cooking them.
This is a square egg press. If you don't want your eggs to roll around (or if you want to fool some naive person into thinking there are square chickens), you can buy one here.
I think the most relevant things we learned was the power and versatility of eggs. They serve so many purposes:
1) As a main course! You see this a lot in breakfast.
Chef Morse demonstrated the difference between an American omelette and a French omelette. Basically, the French omelette is cooked to be less well-done (a bit runny). I think people tend to overcook eggs - usually when they're still runny you can finish them off the heat because they will still cook for a little.
2) The yolk can be combined with cream to form a liaison (ha, ha). A liaison is generally added to soups or sauces to thicken them and add color/richness. Alfredo sauce is an example.
3) The yolk contains lecithin, which is an emulsifying agent (able to keep fat/oils and other ingredients in uniform suspension). You'll see this process at work in dressings and things like mayonnaise - without an emulsifier the oil would just separate from the other ingredients.
4) When beaten, the liquid can be used as a binding agent. For example, when making breaded cutlets you would dip the meat in flour to coat, then the egg mixture, then breadcrumbs (or other crust agent).
5) The whites can be used as a clarifying agent. So far I've only heard of it being used when making consomme (richly flavored clear soup made from stock), something about the egg proteins allowing the solid bits in the stock to congeal at the surface so they can be skimmed off.
6) The whites can also be used as a leavening agent. This is illustrated by the almost-cooked omelettes we finish off in the broiler (they puff up), but more famously in souffles.
These are the ingredients for a souffle omelette (the egg yolks and egg whites having been beaten separately, then combined before entering the pan). The result is a puffy, creamy omelette.
Aside from all these amazing uses for eggs, a few tips about buying and using them:
1) If the recipe doesn't specify what kind of eggs, assume large eggs.
2) Always check the eggs to make sure they are clean, uncracked and uniform in size.
3) Eggs are graded AA (freshest, highest quality), A, or B. Depending on what you're making, the grade can be very important. For poached eggs you'll want grade AA eggs because they contain a greater amount of thick egg white, which will cling to the yolk when cooking and result in a successfully poached egg. As eggs get old, thick egg white gets turned into thin egg white, which leads to grade B eggs that are very runny and not good for much except for scrambled eggs or for baking.
4) Always store eggs in the refrigerator. If you store them at room temperature, they will drop one grade a day.
5) Because the typical egg shell has 17,000 pores, eggs absorb odor easily, so don't store them next to smelly things!