Until the turn of the 20th century, family surnames were not in common use in Sweden. Instead, most Swedes followed a patronymic naming system, practiced by about 90–95% of the population. Patronymics (from the Greek pater, meaning "father," and onoma, for "name") is the process of designating a surname based upon the given name of the father, thus consistently changing the family surname from one generation to the next.
Using Gender Distinction
In Sweden, -son or -dotter was usually added to the father's given name for gender distinction. For example, Johan Andersson would be the son of Anders (Anders’ son) and Anna Svensdotter the daughter of Sven (Svens’ dotter). Swedish son's names are traditionally spelled with a double s—the first s is the possessive s (Nils' as in Nils' son) while the second is the s in "son." Technically, names that already ended in s such as Nils or Anders should have three s's under this system, but that practice wasn't often followed. It is not uncommon to find Swedish emigrants dropping the extra s for practical reasons, to better assimilate into their new country.
Swedish patronymic "son" names always end in "son," and never "sen." In Denmark the regular patronymic is "sen." In Norway, both are used, although "sen" is more common. Icelandic names traditionally end in "son" or "dotir."
Adopting Nature Names
During the latter-half of the 19th century, some families in Sweden began to take on an additional surname to help distinguish them from others of the same name. The use of an extra family surname was more common for people who moved from the countryside into the city where long-term use of patronymics would have resulted in dozens of individuals with the same name. These names were often a composition of words taken from nature, sometimes called "nature names." Generally, the names were made up of two natural features, which may or may not have made sense together (e.g. Lindberg from lind for "linden" and berg for "mountain"), although sometimes a single word would make up the entire family name (e.g. Falk for "falcon").
Sweden passed the Names Adoption Act in December 1901, requiring all citizens to adopt heritable surnames—names that would pass down intact instead of changing every generation. Many families adopted their current surname as their hereditary family surname; a practice often referred to as a frozen patronymic. In some cases, the family just chose a name they liked—such as a "nature name," an occupational surname related to their trade, or a name they were given in the military (e.g. Trygg for "confident"). At this time most women who were using patronymic surnames ending in -dotter changed their surname to the male version ending in -son.
One last note about patronymic surnames. If you are interested in DNA testing for genealogical purposes, a frozen patronymic does not generally go back enough generations to be useful for a Y-DNA surname project. Instead, consider a geographical project such as the Sweden DNA Project.