We want to travel by [fast] train from Madrid to Toledo, then continue on to Andalusia, as recommended in Rick’s Best Three-Week Trip to Spain. However, maps seem to indicate that the fast train doesn't travel to Toledo. Nor does it continue on south from Toledo to Seville. Rather it appears that one must go back to Madrid -- in fact one source we read said that very thing. Can anyone please confirm how train transportation works through Toledo going further south?
There is no and was probably no need for high speed service from Madrid to Toledo as a regular train only takes 33 minutes. Almost like going to the suburbs of Chicago. Toledo is in the same region as Madrid though a map makes it look far.
Yes you have to go back 30 minutes on the train north from Toledo to Madrid to go south to Seville on the high speed rail service.
Yes, how the bullet train system works in Spain is that "all lines lead to Madrid", so to speak. While there is an AVE train that goes to Toledo, it does not continue down to Andalucia, you will have to backtrack up to Madrid change trains at Atocha station for Cordoba/Sevilla. You can see the High Speed lines by this map - https://en.wikipedia.org/wiki/AVE#/media/File:HighSpeedSpain.svg
Toledo's on a spur line from Madrid, used by commuters and tourists. Allow half an hour to transfer in Madrid, the station is large and some people find it confusing. It's a good idea to buy your tickets to/from Toledo a day or two in advance since trains often sell out.
The best option is go to Madrid with AVE Train (high speed train) and there you can take another AVE to Cordoba. Is the fast trip possible. You will be in Cordoba in 2h and 30 min.
In Cordoba you have to visit the Mezquita https://mezquita-catedraldecordoba.es/ and enjoy a typical andalusi bath