Annotated chess game

Not anymore

Many people also protect the pawn by d3

It is a good move but with careful play, black can get an even game.

It is a good move. True, you don't see it often at the top level, and that is owing to Black's ability to equalize - something thrashed out over the centuries ioto well known theory. Yet there is always room for innovation, and at the level you are playing at, you can test your opponents' defensive skills with the Moller attack (4.c3 and 5.d4) or the Evans Gambit (4.b4), say. Then, you never know, Black might try the Two Knights' Defence (3...Nf6), which can lead to all sorts of excitement, including the Fried Liver attack (4.Ng5 d5 5.exd5 Nxd5? 6.Nxf7!) or wild ride of the Traxler (4.Ng5 Bc5!!??).

Yes i've heard of the fried liver.

For people that don't know alot about opening, this is much safer than 3...Nf6.

But I reckon 3...Nf6 is more fun...  

What do you mean by it is more fun and thanks ianadowman for the diagram as it helps explain the moves you have listed in the last comment on this annotation.

Here, best is c3 taking the initiate.

The move played is the Guioco Pianissimo - very unassuming, but solid. A freer game can be obtained by 4.c3 (or 4.b4!?), but maybe the move played can give more reliable and longer lasting prospects.

I feel safe in this position.

I don't think this is a good move, if Black does castle white is at a disadvantage as Black can push back the knight with h6, gaining a tempo.

where is the rest of the game??

This is just an example of how many of my games begin.

Pity the thing ends here: it is just a stub. Having said that, Black's move effectively refutes White's 5.Ng5 as that piece is now doing nothing in particular, and will soon have to drop back to f3, costing White at least one, and probably two, tempi. In my earliest days, I used to play this, specifically with the idea of taking on f7 even if Black castled, relying on the equality of R+P and N+B. This was also predicated on my being able to handle major pieces better than the minor. But, really, this was bad strategy. Look at the position after such an exchange: w Black has a big lead in development and the more active game into the bargain; and the King is hardly discommoded by its present location. I soon learned not to play this sort of thing.

In addition to what ion said, according to Larry Kaufman, a minor piece is worth about 3.25 pawns, and the bishop pair is worth 0.5 pawns, so white is also down about a pawn's worth in material.