Do You Eat The Greeen Part (tops) Of Leeks?

Yes they are very good to eat and have a pleasant flavour.
Depending on how you want to cook leeks there's no reason why the green part shouldn't be included. The texture is more course than the white part but if cooked properly they're really good. You can also grate this green part and put it with or into salads. If you are making casseroles and stews use all the vegatable for a good flavour.
If you are braising the leeks, again, there's no reason why the green part should be disguarded. Just ensure that the green part is cooked for long enough until it's the right texture for your own tastes.
Be sure to wash the green part throughly as it can retain the earthy bits.
They're also nice with white or cheese source .As a personal  preference I prefer the green part of the leeks and always use them as I would the rest of the leek.