d4 in general is stronger than d3 - you claim additional central space and force black to defend his e-pawn. It's the only real try for an advantage. However, after the immediate d4, bg4 equalizes since it's hard for white to defend the pawn without advancing it and prematurely locking the center. Thus h3, preventing bg4 and threatening d4 on the next move.
Learning Ruy Lopez

How do you think h3 jeopardizes king safety? Black doesn't have any looming attack on the king side. As shoop2 said, h3 prevents the Bg4 pin, thus making d4 a stronger threat for white.
Just for the record, though, d3 is by no means a BAD move there. The Ruy is quiet enough at this stage that as long as you're playing thematic moves, it's almost hard to go too far wrong. Depending on the order and selection, you close certain doors and open others.
Go with d3 here, and you're more or less committed to playing it in a certain slow, positional style.
Although, if that's your cup of tea, you might find it easier to understand and with fewer testing replies from black, if you approach it via an Italian move order.

Thank you both so much! I believe I really do understand now. It all seems to boil down to being able to see several moves ahead, and I don't yet have the ability to do so without a bit of help. Thanks again.

Thank you both so much! I believe I really do understand now. It all seems to boil down to being able to see several moves ahead, and I don't yet have the ability to do so without a bit of help. Thanks again.
No offense, but it sounds like you're not up to the level where you should be studying openings like this yet. If you play the Ruy Lopez against other beginners, there's really not much chance that they'll follow the main line through 9 moves, anyway. That's why it's more important to understand how to pick a move than to memorize an opening sequence this deep.

If you like d3, look for the game Karpov-Spassky 1973, though the level of play in that game is pretty insanely high, it shows a lot of amazing positional ideas as Karpov slowly picks apart the former world champion.

Thank you both so much! I believe I really do understand now. It all seems to boil down to being able to see several moves ahead, and I don't yet have the ability to do so without a bit of help. Thanks again.
No offense, but it sounds like you're not up to the level where you should be studying openings like this yet. If you play the Ruy Lopez against other beginners, there's really not much chance that they'll follow the main line through 9 moves, anyway. That's why it's more important to understand how to pick a move than to memorize an opening sequence this deep.
I think you're correct, in that I am still very much a beginner and probably should not bother much with openings at the moment. But I am having fun trying this stuff, and this thread has been very helpful to me. My thanks to everyone for their comments.

What I like about H3 is how it gives the white King an escape route incase a rook got down there for example. If the pawn was still on H2 and the king was still on G1, resting behind 3 immobile pawns then checkmate if a Queen or Rook were to get down there and you had no defense for the King.
Thank you both so much! I believe I really do understand now. It all seems to boil down to being able to see several moves ahead, and I don't yet have the ability to do so without a bit of help. Thanks again.
No offense, but it sounds like you're not up to the level where you should be studying openings like this yet. If you play the Ruy Lopez against other beginners, there's really not much chance that they'll follow the main line through 9 moves, anyway. That's why it's more important to understand how to pick a move than to memorize an opening sequence this deep.
I think you're correct, in that I am still very much a beginner and probably should not bother much with openings at the moment. But I am having fun trying this stuff, and this thread has been very helpful to me. My thanks to everyone for their comments.
There is no place in chess for fun.
What I like about H3 is how it gives the white King an escape route incase a rook got down there for example. If the pawn was still on H2 and the king was still on G1, resting behind 3 immobile pawns then checkmate if a Queen or Rook were to get down there and you had no defense for the King.
Nimzowitsch would smile, if he weren't extremely dead.

What I like about H3 is how it gives the white King an escape route incase a rook got down there for example. If the pawn was still on H2 and the king was still on G1, resting behind 3 immobile pawns then checkmate if a Queen or Rook were to get down there and you had no defense for the King.
Nimzowitsch would smile, if he weren't extremely dead.
I don't know if that's a compliment or not...but thank you any how. And yes it is a shame he is so intensely dead.
What I like about H3 is how it gives the white King an escape route incase a rook got down there for example. If the pawn was still on H2 and the king was still on G1, resting behind 3 immobile pawns then checkmate if a Queen or Rook were to get down there and you had no defense for the King.
Nimzowitsch would smile, if he weren't extremely dead.
I don't know if that's a compliment or not...but thank you any how. And yes it is a shame he is so intensely dead.
Nimzo was extremely bullish on prophylaxis. In quiet positions, where you could kind of sort of maybe justify a move, AND it also happened to do things like give a possible down-the-road flight square for your king, he would sing the praises of such moves as though he had just re-discovered Greco's mate.

I think your question was a good one it shows that you are thinking. Your right that h3 weakens White kingside pawn structure. In many positions h3 would be a mistake for that reason. However, as has been pointed out Black is in no position to mount a kingside attack. Black's counter-play is on the queenside and it would be a strategic mistake for him to try to mount a kingside attack.
I think you are also wise to not take up the Ruy Lopez at this point. Stick to open tactical games like the Italian, Bishop's opening, and the Vienna. The Ruy is a complex, subtle, opening that is much easier to play from the Black side.

Yeah, I'm not a big fan of the Ruy Lopez for beginners, either. I'm rated 1700ish USCF, and I still prefer the Italian as white. That bishop pointed at the weak f7 square immediately just leads to all sorts of fun tactical possibilities. Decent opponents don't let me get any tactics out of it, but the threat of tactics is often enough to force weaknesses in the opponent's position.
Hi all, Great tips for a beginner, especially:
@ Fromper ...That's why it's more important to understand how to pick a move than to memorize an opening sequence this deep.
and
@ blake78613 ...Stick to open tactical games like the Italian, Bishop's opening, and the Vienna. The Ruy is a complex, subtle, opening that is much easier to play from the Black side.
Could you suggest any education material regarding the Understanding how to pick a move ?
Can someone explain to me why 9. h3 is a good move in this game? It seems to jeopardize king safety for no good reason. I would be tempted to try 9. d3 to provide support to my fellow pawn. I am new to learning openings, and am trying to understand the reasoning behind the moves.