Why on this opening does white castle first?

So I've been looking through the game explorer at this situation as I've ended up here several times. Although I'm not good with opening names yet I believe this starts as the Ruy Lopez for white.

My question is why is white's most common response here to castle instead of do d3, Nc3, or Qe2? If you follow the next few most common moves if the knight takes the center pawn ends up with white trading a rook for a bishop. To this inexperienced player that doesn't seem like a good situation to be in. I tend to do Nc3 because I am afraid of losing that rook and it puts my in a position I am more comfortable playing.

Here is what the next few most common moves results in.

Is there a reason why this is a good result for white?

The reason the bottom diagram is good for white is the fact that he has two minor pieces for a rook and a pawn. This is a good exchange. While the numbers in the traditional piece value are equal, the fact that two minor pieces can coordinate and hit more than the single rook can protect makes it a good trade.

The two minor pieces take a lot more time to get into ideal position than a single rook, so sometimes it is very hard to coordinate the two pieces in a practical game. Therfore, it is not all roses and rainbows to have the trade so it is still very much a game.

Don't shy away from getting this imbalance of having two minor pieces for a rook or a rook and a pawn because it is very good practice.

 That makes sense. But in that second diagram black can easily get his rooks connected along with easily being able to take control of the e and f file. Also white doesn't have a lot of maneuverability of his knight on d2 which is also blocking his bishop on c1.

Is black's position better than white's here?

White does have pressure on h7. White also has the possibility of putting pressure on the c3-f8 diagonal. Black has weak dark square coverage and just lost its black square bishop.

Maybe the positions are fairly equal, but overall this seems like an uncomfortable position for me if I am white.

I do not know who is doing better in the second diagram. That is a really odd position. Can you please provide the moves that you claim commonly get you into that position?

The reason white castles in the first diagram is because he can. White wants to castle and play c3 and d4. That is his dream. Notice how all but Qe2 gets in the way of that plan?

The queen does not want to go to e2. Moving the queen there, then castling, then moving the queen elsewhere is just a waste of time. 

You mention that the rook commonly trades for a bishop which I believe is not true. I do not know where you get your information, but if you show me the moves I will show you where you are probably going wrong.

 I got these moves by stepping through the game explorer. The knight taking the center pawn is the second most common master move in the top diagram, from there the rest of the moves I go through are the most common.

The position is complex but white can avoid that with the more popular 9.Nd2 and if Bc5 then 10.Nxe4 leads to a semi ending where white scores well (but black is ok if he plays correctly). 5.0-0 Nxe4 is called the open defence. It's a strong  defence but certainly not the refutation of 5.0-0 :) If you are not comfortable with allowing it you can play the quieter 5.d3 which has been played by several strong GMs (including Carlsen) and contains some poison, and switch later (or never if you happen to like 5.d3) to the more critical but also more complex 5.O-O.

I don't think more popular is the correct term there unless the game explorer on this site isn't correct. The most popular move choice on explorer for 9 was c3.

That is why I'm so curious about it.  On my first diagram d3 seems nice since it opens up the black square bishop while defending the pawn and you are still in a good position to castle. I recently switched from doing Nc3 on the opening diagram to trying out d3 and I did like the feel of it.

Fortunately most of my opponents have been playing e5 instead of the sicilian which is allowing me to practice different approaches to the opening.

I'd like to learn why the second diagram is such a strong position and why more masters choose to castle on 5 and why they choose 9. c3 over Nd2 which puts pressure on black's knight.

The position in diagram #2 is heavily analyzed (Dilworth attack). With best play for both sides it's slightly better for White (close to equal). But the whole variation is not critical currently for the Open Ruy Lopez.

Nobody forces you to play 5.0-0 of course. 5.Nc3 is fairly harmless (the c3 square positionally is desirable for a pawn), 5.Qe2 is the Worral Attack, which is not very popular (with a good reason) while the Steinitz system (5.d3) is quite poisonous, and requires good play by black. McDonald recently wrote a book on the Ruy, in which he deals at some detail with the Steinitz pawn formation.

 Do you happen to know where any of that analysis is? Books or articles for example?

That book sounds interesting I might see if I can find it, sounds like a good read.

McDonald's book is fairly recent, and it's called "Ruy Lopez move by move". It's a good book, not so much about variations, but explaining the positional elements of the opening.

There's also a recent repertoire book based on the Worrall by Andrew Greet (2006), which I found disappointing (no surprise, the author has not played a single game on the variation by the time he wrote it).

No other sources about the Steinitz I know about. Just have a careful look at some games by super-GM's Nepomniachtchi, Morozevich and Ponomariov, who employ it frequently.

Paulgottlieb hit the nail on the head: after 4...Nf6 white knows for certain that he want to castle, soon or later. Instead he is not so sure that he wants a pawn on d3 (he might want it on d4) or a knight on c3 (he might want that square for a pawn to support d2-d4 and create a retreat square on c2 foe the light squared bishop). As a result 5.d3 and 5.Nc3 are perfectly reasonable and playable (5.d3 in particular is far from innocuos) but it makes sense to play 5.O-O, because white retains more options in the centre and is allowed to choose the best setup according to black answer. This is why the move is the most popular and probably the strongest. However the other side of the coin is that black also has more options after 5.O-O(such as taking on e4). As a consequence 5.d3 is quite a bit simpler to play, and a perfectly reasonable choice.

Wise words, Bresando. 5.0-0 is by far the reasonable and most natural white move, and 5...Nxe4 (the Open Ruy) is just another Black response white has to counter.

I have played the Open Ruy in the past a few times, but I have abandoned it, because I believe Black can play the Ruy in less commital ways. I have used the Open Ruy against two GM's- namely Kotronias and McDonald. Against McDonald I had a perfectly resonable position until I made a horrid strategical blunder, and I had a lost position (somehow I scambled a draw, with alittle help from my GM friend), but Kotronias mercilessly exploited my middlegame inaccuraties, and slaughtered me.

Thw Open Ruy is still VERY playable, and an active way to handle the Ruy. But it's very commital, and black has to be on the alert to justify the positional concessions he has made.

Thanks for the insights everyone. It seems like the best move for my skill level would be d3, but O-O is something I should explore as I get better.