Iceland became independent in 1945[0]; in 1918 Iceland became a sovereign state under the rulership of the Danish king[1].

The Independence Party is center-right (very conservative for Iceland) and was formed in 1929 advocating for full independence of Iceland. They haven't changed their name since. It's been one of the four major political parties of Iceland since inception and more often then not the largest; every head of the party has been prime minister at some point (except the current one; that might change in the next week as they are in coalition with the just-resigned prime ministers party and there is a void to fill). In short you could say that they are pro-business and for smaller government. The overview here [2] is a good start, but you can go straight to the source here (english below) [3].

[0] https://en.wikipedia.org/wiki/Founding_of_the_Republic_of_Ic...

[1] https://en.wikipedia.org/wiki/Danish%E2%80%93Icelandic_Act_o...

[2] https://en.wikipedia.org/wiki/Independence_Party_%28Iceland%...

[3] http://www.xd.is/um-sjalfstaedisflokkinn/

Political party names can be fun. In both Norway and Denmark there are liberalist right-wing parties called "Venstre", which literally means "left" (as in left-wing). Because they were, relatively speaking, left-wing 130 years ago.

In Australia, some (including myself) would argue that our Liberal party is decidedly not very liberal...

Not even in the old sense of the word.