An “independent school” (friskole) is an alternative to the public school (folkeskole). They have been created on the basis of Article 76 of the Constitution (Grundlov) which says that in Denmark we have a duty to learn, not a duty to go to school. There are 550 “independent schools” that operate under the “Independent Schools Act”. In comparison, there are 1066 public schools. Read more here.
Each “independent school” decides on its own value foundation – some schools follow the Grundtvig tradition, others the Rudolf Steiner, some are multilingual (French and German schools, f.ex), some are faith-based (Muslim, Catholic, f.ex) and so on.
The “independent school” is financed via state subsidies (76% of the average government operating grant per year per student, which is 52,578 DKK) and parent payments (which average 15,000 DKK per year).
The reason behind so many new applications for “independent schools” is that local governments are forced to close small schools (due to cuts in spending), usually placed in villages. So, the communities rally to create partly state-financed “independent schools”.