Bokmål is the most common with 80 to 95% of the population speaking this as their first language. It is based on Danish but with a Norwegian flavour, and stems from when Norway was ruled by Denmark, with Danish being the language of the elite, used in courts and for other administrative purposes. Bokmål, which means “book language”, has evolved separately from Danish, and although they are mutually intelligible, they are two separate languages now.
Nynorsk (new Norwegian) is the language spoken by the remainder of the population. This language is based on the way the rural population spoke rather than how the ruling classes spoke.
The two languages together have about 5 million speakers. Both languages are taught in school, but students can choose which one they specialise in. An idea was put forward in the past to unify the two languages to create one Norwegian language, but it never really took off.
If you fancy leaning a little Norwegian, try this free course from FutureLearn.