The history of Denmark goes as far back as the age of the Vikings. What concerns the era of the 18th century is very limited in the way of information about the kingdom's rulers. I have found a few resources on the kings of Denmark, however, these are very limited.
Denmark today is a limited Constitutional Monarchy. The Kingdom of Denmark in the 18th century included Sweden, Norway and Denmark. The period between 1536 and 1720 saw many changes. Economically and socially, the period can be divided into two halves. The 16th century was a period of boom, but around 1600 a trade crisis set in. The crisis deepened during the following decades and became a long-term slump that only began to diminish around 1740.
To learn more about Danish history, read the following essays. Both essays come from the GlobalSecurity.org website.
Reformation and Absolutism
This essay covers the period from 1536 to 1720. In this essay, you will learn what life was like, the form of government, and the development of Absolutism and foreign policy during this period.
The Long Peace and the Short War, 1720-1814
This essay examines the remarkable history of Denmark.
As promised, here is the timeline of 18th-century Rulers of Denmark. All monarchs here were after the Union of Kalmar.
Rulers
Frederick IV (1699-1730)
King of Denmark and Norway from 1699-1730; son of Christian V; freed the serfs in 1702.
Christian VI (1730-1746)
Frederick V (1746-1766)
Christian VII (1766-1784)
King of Denmark and Norway, born in Copenhagen; son of Frederick V, whom he succeeded in 1766; mentally weak, dominated by schemers.
Frederick VI (1808-1839)
King of Denmark and Norway; succeeded 1808 (previously regent); joined Armed Neutrality of North (1800) and was punished (1801) by the destruction of the fleet by English and (1807) by the bombardment of Copenhagen; formed alliance with Napoleon and was compelled (1814) to surrender Norway to Sweden as punishment.
(regent 1784-1808) (Norway annexed to Sweden, 1814)