Train between Madrid (Atocha station) and Granada

Train schedules are generally released 90 days in advance, sometimes less than that. Start checking 90 days prior to the date you want to take the train.

Thank you. I'm at about 60 days out and there are no schedules that I can see.
Is it correct that there is a high speed train between Madrid and Granada? What I am reading says there is but getting concerned.

I tried a random date in the middle of April (4/16) and the IRYO site is allowing me to buy tickets for that date.
Trains from Madrid to Granada on IRYO seem to all require a change in Cordoba.

One of several options on that date in April leaves Atocha at 11:15, connects ion Cordoba, and arrives Granada 16:49.
So this is a rather long ride....maybe RENFE has direct routes.

Using the Renfe app, I looked at 23 April and there are four Madrid to Granada departures listed; three (Ave) you’d be interested in. Each takes about 3.5 hours. Their departure times were 07:20, 13:35, 19:50. The last two had the fewest stops. The times were the same for each day I looked at.

The schedule goes out through the entire month.

Last week I was able to buy a train ticket from Madrid to Sevilla on Renfe. But to get from Sevilla to Granada and then Granada to Madrid I had to buy on Rick Steves' site. These are all for April.

It could be due to the train derailment. I purchased my train tickets in early January for late April. (Madrid - Cordoba, Cordoba - Granada, Granada - Seville)

Thank you all for your feedback. I have figured out my trains.

Any thoughts on whether I should do Madrid, Granada, Sevilla in this order OR
is Madrid, Sevilla, and then Granada better?

I don't think it matters. Do the routing that is most convenient.
What is the total plan? Where are you flying out of in the end?

Take a look at the schedules into and out of Granada; frequency is rather thin there. Perhaps the schedule will work better for you in one direction or the other.

I’m looking for Madrid to Toledo tickets for mid April. I check several sites including Trainline with all saying nothing was available. I tried iryo, ave, and renfe.

Renfe releases tickets when it feels like it. You just need to wait. You need not fear that tickets to Toledo will sell out instantaneously. Since you're traveling around Easter, you are smart to be checking early, because it's possible some individual trains will turn out to be super-popular. But don't stress about it now.

Tickets are currently available through March 31, so it's possible early-April tickets will go on sale at the beginning of February (no promises; Renfe is inconsistent).