Eggs are a most complete food. They contain everything that is necessary to make a complete little bird.
Eggs are also quite easy to obtain. Chickens can even be kept in a very small yard. No wonder that eggs are so very popular all over the world.
The basic preparations of eggs for the breakfast table are boiling/poaching; pan-frying (scrambled, omelet) and baking. With each of those, the eggs can be cooked anywhere from soft to hard. When you start adding other things to the eggs, you get literally thousands of possibilities.
This is just a general overview and classification of things I have prepared myself. For a more comprehensive listing, see Wikipedia's List of egg dishes
These are only a few of literally hundreds of possible uses of eggs in the kitchen.
My preferences are soft yolks all around: soft-boiled, sunny-side-up, and soft-scrambled.
That doesn’t mean I won’t eat the others. I like deviled eggs with moderation. Dry-scrambled eggs are better for tortilla wraps, because leaky tortillas are no fun. When I am feeling adventurous, I may even try poaching, even though I’m not very good at it. :-)
I have listed the same cooking method order here as for meats. It is pretty much the reverse of my original order by popularity / frequency of what I do at home. Just start at the bottom.