What European countries do not have a railway?

This is a little tough, trying to research & find correct answer. So far, looks like Katmandu..but not sure if that is answer. I will continue to research..

While the railway systems within Europe and also within North America all interconnect (albeit sometimes with incompatible technology), Africa, South and Central America, Asia and the Middle East generally do not connect very well. This might be called "rail-locked". Kathmandu, for instance, the capital of landlocked Nepal, does not have any railway connection over the Himalaya passes, unlike Tibet.

https://en.wikipedia.org/wiki/Landlocked

There are no railways in Andorra, Cyprus, Faroe Islands, Gibraltar, Iceland, Malta and San Marino.

https://en.wikipedia.org/wiki/Inter_Rail

Kathmandu, Nepal is in Asia, not in Europe.

The previous answer is as good as correct, but you might add the Channel Islands of Guernsey and Jersey. The only Channel Island to have a working railway is Alderney.

https://en.wikipedia.org/wiki/Guernsey

Jersey does have a preserved railway, but it's only got 1/3 mile of track at present. http://www.pallotmuseum.co.uk/railway/index.htm