First, find out where the southernmost and northernmost train stations in the EU are located. Technically, the southernmost railway station is Pozzallo on the Italian island of Sicily, but Pozzallo is not on the mainland and rail services to and from coastal towns have been greatly reduced to almost non-existent. (Trains have been almost completely replaced by buses), so consider that the city of Algeciras in Spain is the southernmost railway station in the EU.
Contrary to popular belief, the northernmost railway station in the European Union is not Narvik in Norway, as Norway is not a member of the European Union. The EU's northernmost train station is located within the Arctic Circle in Wasshyaure, Sweden. However, there are currently no passenger trains running to Wassihaule, so the next northernmost railway station is Riksgransen, a town directly next to Wassihaule.
Neither Algeciras nor Riksgransen are large rail hubs and are understandably very far from each other, so you can't expect to get from one to the other quickly. That said, the following itinerary involves his four nights, two of which are spent on the train, which is one of the quickest and most convenient ways to travel by train. (Please note that this itinerary is evergreen and does not include seasonal routes.)
Segment 1: Spain (from $173)
- Algeciras to Antequera Santa Ana (Málaga)
- Antequera – Santa Ana (Málaga) to Madrid – Puerta de Atocha (using high-speed train AVE)
- Madrid – Puerta de Atocha – Barcelona Sants (via high-speed train AVE)
In Barcelona, stay in one of the city's excellent Airbnbs or hotels.
Sector 2: Spain to Sweden (from $461.50)
- Barcelona Sants → Paris Gare de Lyon (using high-speed train TGV INOUI)
- From Gare de l'Est to Frankfurt am Main Central Station (by high-speed train ICE)
- Frankfurt am Main Central Station to Hamburg (night high-speed train ICE)
- Hamburg to Copenhagen H (Eurocity train)
- Copenhagen to Stockholm (using high-speed train SJ)
In Stockholm, spend the night at the city's best Airbnb.
Leg 3: Sweden (from $76.50)
- Stockholm to Riksgransen (overnight on sleeper train VY) Please note that due to a track derailment, this section will not be operated again until June 18, 2024.
Although this train journey is spectacular, it can be exhausting and expensive. That said, if you're up for a challenge, it's completely doable and you can try out a wide variety of trains and train operators. You can plan and book this itinerary using RailEurope and Eurail, but you will need to split it into several segments. Additionally, if you are a Eurail Global Pass holder, all sections of this itinerary are included. 
