Of course this is called the Giuoco Piano, which you can find on wikipedia, here.
What To Play!

no it is only the giuoco piano if i play Bc5 and then I dont like that because they get the iniative and centre with c3!

1 e4 e5
2 Nf3 Nc6
3 Bc4 Nf6
4 Ng5 d5
5 exd5 Na5
This is mainline Two Knight's Defence and perfectly sound.... one of the recognized texts is "The Two Knight's Defence" by Yakov Estrin.
other variations include:
5... b5 (Ulvestad's Vatiation)
5... Nd4 (The Fritz Variation)

yes I knew about all of them and at my level if you gain a pawn immediatly in the opening then....!
So.... you would prefer a second-rate move that is also good? I don't understand. Seriously, if you intend to play the two Knight's Defence, you need to buy a book...guessing moves just won't cut it.

It's the bible where 2KD is concerned... a small, compact book, should be fairly cheap... may be able to get it second hand for a song. The copy I have was part of the "Chess for modern times" series, published by Chess Ltd, sutton coldfield, England. I think Chess Ltd. has now folded (B H Wood (the owner) long passed on), however, I'm sure Batsford or Pergammon will have a copy.
http://en.wikipedia.org/wiki/Yakov_Estrin

Freddie,
took some finding, as the book is probably out of print now:
http://www.amazon.co.uk/Two-Knights-Defence-Yakov-Estrin/dp/0903500094/ref=sr_1_2?ie=UTF8&s=books&qid=1229253262&sr=1-2
I have a really good group of openings I play but there is one thing as Black which has been annoying me for so long. For the last month, I have being playing a trap line and even though I have won 2 games through it, it is horrible for me if they don't fall for it!
The line is as follows: 1. e4 e5 2. Nf3 Nc6 3. Bc4 ??
If I play Nf6 then they can play Ng5 and they automatically win a pawn unless I accept the pawn on d5 with the knight which is just not going to happen.
(I presume people know what I am talking about here!)
If I play Bc5 then they play c3 and I hate playing against The Giuoco Piano or The Evans Gambit if they play that!
I have been trying Nd4 and if they take the pawn on e5 then I win straight away with Qg5 but if they take the knight on d4 then I have a horrible position.
What should I do....P.S. I dont want to change my first two moves so please dont suggest that for certain reasons I am not going to go into now!....please i am really struggling with this and I dont know what to play ahhhh!