The township of Lillehammer is located around the northern part of lake Mjøsa, the biggest lake in Norway. It consists of the city of Lillehammer and a surrounding rural area. The city is the 'capital' of Oppland County (earlier called Christians Amt) in the eastern part of southern Norway. Lillehammer is the 'gate' to the valley of Gudbrandsdalen and is surrounded by the following townships:
To the south and on the western side of the lake is Biri (now a part of the township of Gjøvik). To the east and south (and on the eastern side of the lake) is Ringsaker in Hedmark County. To the north is Øyer, and to the northwest and west is Gausdal.

Many Americans are confused by the use of the names Lillehammer and Fåberg (earlier written Faaberg). The use of these names has changed during the history and I will try to give a short explanation of this.

Before 1827 Fåberg was the name of a parish that covered exactly the same area as today's township of Lillehammer. The city of Lillehammer did not exist, and Lillehammer was the name of a farm in Fåberg parish like any other farm. But Lillehammer was also the name of parish of ease inside Fåberg parish with its own church built on the Lillehammer farm.
In 1827 it was decided to build a city at the northern end of lake Mjøsa. The city was built on the grounds of the Lillehammer farm and thus named Lillehammer. Ten years later, in 1837, a local authority called kommune (township) was established and these townships covered the same areas as the corresponding parishes, i.e. Fåberg township equals Fåberg parish.
Eventually the city of Lillehammer was split from Fåberg township and formed a township of its own. This new township of Lillehammer covered just a very small area and was completely surrounded by Fåberg on all sides.
This was the situation until 1964 when it was decided to reunite the two townships. However this 'new' united township was called Lillehammer and not Fåberg as it had been called at all previous times. Today Fåberg is the name of a small suburb of the city of Lillehammer located a few miles north of the city center but still inside the borders of the township. This means that today's township of Lillehammer is identical to the earlier Fåberg parish and township.