Lasagna is a popular oven-baked pasta dish of fresh egg pasta squares. It is a traditional dish from Bologna in Northern Italy, where the sheets are always green through the addition of spinach or nettles to the egg dough. In Bologna, these home made sheets are layered with small amounts of real Bolognese ragù (made with both beef and pork, very little tomato and no southern herbs like oregano and basil but a little nutmeg instead) and simialrly small amounts of "besciamella" or béchamel sauce in an oven dish. There are at least 5 layers of pasta dough, and the layers stay separate and do not "merge" together into a mush. A light sprinkling of Parmigiano-Reggiano , and a few dabs of butter end the dish which is then baked for about half an hour. The use of Mozzarella in place of Béchamel suggests a Neapolitan variation to the original Bologna classic, as does the use of Ricotta.
Lasagne refers to multiple sheets of pasta; lasagna refers to the dish or to individual sheets of pasta.
In Italy but especially outside, many lasagna variations exist today. Vegetable lasagna, lasagna without béchamel sauce, lasagna without any sauce (just vegetables and/or meat) or even lasagna without sheets of pasta.
When assembling a lasagna, start with the main ingredient (ragu, vegetables, seafood, etc.), add a layer of béchamel sauce, then one layer of lasagne pasta sheets and then the main ingredient again. Continue until the oven dish is full. End with a layer of pasta, spread some béchamel sauce on top and sprinkle the cheese over it.