It's quite surprising how few opening books for playing the Ruy Lopez as white there are, given that it's one of those lines that have a claim of being "the main line of chess".
Greet's Play the Ruy Lopez is from 2006. Shaw's Starting Out: the Ruy Lopez from 2003. Khalifman had the Ruy Lopez in his Opening for White according to Anand series but it was very detailed, very high level and is also getting old.
Doknjas' Opening Repertoire: The Ruy Lopez was published last year, so it is easily the most recent white report in the Ruy. The writer is an FM, I have no idea how good of a writer he is. Here is a review at the BCF site.
But my vote goes to McDonald's Ruy Lopez: Move By Move for a first book on the Ruy.
Because it is very focused on the ideas of the opening, and it has a plan for how you should start playing the opening: first you play safe lines based on an early d2-d3, which are fine and played by the world top, and then later when you want to you can expand into more and more complex lines by playing d3 later in the game, or never. So it contains two repertoires in the closed Ruy, one with d2-d3 and one aiming for d2-d4.
Only if you are substantially stronger than 2000 OTB, already understand the structures and want ambitious concrete up to date theory, then I would get Doknjas as it is very recent.
And if Parimarjan Negi ever finishes the Ruy Lopez repertoire for Quality Chess he is writing, then that probably becomes THE book for strong players immediately.