If you are coming via Tallinn Airport, you should take the direct bus to Tartu (operated by AS Sebe).
The travel to Tartu takes approximately 2 hours 20 minutes.
And the final bus stop is 50m from Hotel Dorpat in Tartu Center.

It is advisable to buy the ticket in advance via internet ( or in the ticket-mashine in ground level (0-level, one floor below baggage claim) of Tallinn Airport.
Tallinn airport is in estonian Tallinna lennujaam. This station name you have to write in estonian…

Buying the ticket in advance is especially important, if you are coming on Sunday evening – many students are coming after weekend back to Tartu and there might be no free seats available any more.
If you have bought your ticket via internet, you have to print the ticket out yourself. You can do this at your home or at Tallinn airport. The ticket machine at ground floor (0-level, one floor below baggage claim) can print your ticket, if you know the ticket number. Printing there is free of charge.
Also, it is possible to print your ticket at information desk, but this cost 1EUR.

It is possible to go also via Tallin Central bus station, if you take the bus number 2. But this takes approximately one hour more.

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