Travel from Vienna to Mauthausen

Try the website rome2rio.com . They will give you train and bus options.

PLEASE dont rely on Rome2Rio.While it may be satisfactory for seeing transportation options, it is notoriously unreliable for specific planning or booking. The website for Austrian trains is here: https://www.oebb.at/en/

There you can find train and bus schedules and fares, and also make any advance bookings.

A train involves one connection.

The train from Vienna's main station to Mauthausen does require a transfer in Linz. I believe you can also get a bus from Linz to Mauthausen. Both options get you to the Mauthausen train station. The Mauthausen Memorial (the concentration camp) is about eight miles away. I took a taxi. The Mauthausen station is just a stop, not really a station, and it doesn't have a taxi rank. You need to call the taxi. Rick's Vienna book has a recommended taxi and that's what I used.

Bring Kleenex.

You take a direct express train to Linz, departing either from Vienna's main train station or from Western train station.

Then you go by bus 362 directly to the Mauthausen Memorial.
Note that this bus line is not operated after October 26, when the winter season starts.

Coordinate your train travel with the bus schedule given below.

https://www.mauthausen-memorial.org/en/Visit/Visitor-Information/How-to-get-here

I've visited a number of the camps , and the most heartbreaking one was Mauthausen . You will need more than Kleenex when you encounter " The Stairway of Death "