There is a city bus network in Göttingen. Visit www.goevb.de/ for schedules (Fahrplaninformation) and other information. Individual tickets cost €2.30, but a pack of 4 or 8 tickets (Vierer-/Achterkarte) will be cheaper. For children 14 and under the prices are reduced. Vierer-/Achterkarte tickets need to be stamped when you enter the bus; failure to do this may result in a fine. A ticket is valid for an hour from the time of purchase (or stamping), and within that hour can be used on any city bus in any direction. You can buy weekly/monthly passes and books of tickets at Karstadt (a local department store) or the Bus travel center (in the square next to the Altes Rathaus).
The MPI is served by three buses. Take bus #21/22 for "Nikolausberg" from the city center and get off at the "Faßberg" bus stop right across the entrance of the institute. From Monday to Friday the #23 runs from the train station to the Faßberg stop. During the day, all three buses run multiple times an hour, both ways. On weekends the #21/22 run all day, the #23 only the evening.
Traveling by train can be expensive but is generally efficient. There are different prices depending on the train category, e.g. the high-speed ICEs are the most expensive, then ECs/ICs (there is an extra cost for these) and traveling by RegionalExpress (RE), RegionalBahn (RB) or Metronom (ME) is the cheapest. Visit www.bahn.de for special deals and more information.
If you travel by train frequently, it may be useful to buy a BahnCard, which entitles you to discounts on all trips. There is a BahnCard 50 for a 50 % discount and a BahnCard 25 for a 25 % discount. If you want to purchase a BahnCard for both yourself and your spouse, the partner card option will be the the cheapest option. For children (6-17 years) you can buy a Zusatzkarte. Please note that both BahnCards automatically renew for another year if you do not cancel them six weeks in advance. With the BahnCard 25 you can get get further discount if you buy your ticket in advance (Sparpreis).
Moreover, there are discounts if you purchase your ticket in advance. You can get 25 % to 50 % off (roundtrip tickets only!) if you buy your ticket at least three days in advance. Please note that these discounts are subject to some restrictions. For example, there is only a limited amount of discount tickets available, and they are only valid for the specific train connection you buy it for. If you miss your train or one of your trains (due to delays in your connection), you can only exchange your ticket for a 15 Euros fee. Moreover, 50 % discounts are only available if your trip includes at least one weekend night or one weekend travel date. There are also group discounts.
On weekends, Deutsche Bahn offers the "Schönes Wochenende" ticket. For 40 € (=1 person, each other person pays 4 €) up to five adults/children may travel on the entire German train network on local trains only (RE, RB, ME). While this is a very cheap way to travel, especially for groups, it is also slow.
"Quer durchs Land" ticket allows you to travel all over Germany on weekdays, too, also on local trains only (44 € for 1 person, each other person pays 8 €).
"Ländertickets" (for Göttingen: Niedersachsenticket) are valid for one "Bundesland" and all local trains (Niedersachsenticket costs 23 € for 1 person, plus 4 € each other person).