Throughout the 1700's in the World of Lesnaya timeline, Sweden has had considerable success as an overseas colonial power. Swedish colonial efforts were primarily opportunistic, capitalizing on treaties and marginal locations in order to establish colonies in the shadow of the major colonial powers (i.e. Britain, France, Spain, Portugal, and Netherlands).
Sweden successfully established a small settlement on the northern coast of Tobago (called Fort Frederick). Unlike in OTL, the Swedes are able to hold off the attacks from the natives and remain in control of the island. The success of this colony helps establish the Swedish overseas trade that will thrive in the future, giving a needed boost to the agrarian Swedish economy, and fueling nationalistic morale and colonial sentiments in Sweden.
Gold Coast, West Africa (1779).
Sweden purchased from Denmark a handful of trading posts and fortresses in the Gold Coast (OTL Nigeria and Cameroon). Sweden was involved in the African-Caribbean slave trade from 1779 through 1807, when they were pressured by the British to end the practice. Afterwards, Sweden maintained the Gold Coast ports and took a keen interest in establishing trade and diplomatic relationships with the local peoples.
Tasmania and Austalia (1801).
A Swedish colonial fleet of 7 ships lands on Tasmania and establishes the settlement of Örnö. Famed Swedish explorer Thorwald Svanholm meets up with the fleet and settles in Örnö. Svanholm is unable to restrain his explorer's spirit, however, and, in 1802 resettles with his wife and children on Flinders Island. However, he would later join a small company of Tasmanian Swedes in founding a settlement in southern Australia, and is chosen to ceremonially plant the Swedish flag and claim the land in the name of Sweden. By 1811, Svanholm will have moved twice more, eventually ending up in a small village in the center of the southern coast of Australia (which is named Svanholm in his honor).
From 1815-1820, the Tasmanian colony is briefly referred to as "Svensland," after King Sven I, and Swedish possessions on the Australian mainland are subsequently referred to as "New Svensland." However, the name "Tasmania" proved to be too ingrained among the settlers, and the official name reverts to this in 1820. However, New Svensland continues to bear its name until the present.
The Australia War broke out between Sweden and Britain in 1826, and resulted in the British conquest of New Svensland by 1829. However, Britain allowed Sweden to retain possession of a truncated portion of Australia (roughly corresponding to OTL Victoria), which did not include the village of Svanholm. Although Thorwald Svanholm had died and been buried outside the village of Svanholm in 1821, and despite repeated Swedish requests, his remains were not exhumed and transferred to the site of his Flinders Island residence until 1887, at which point his residence was named a national memorial.
Conquest of Denmark-Norway (1814).
As Napoleon's army was occupied with an ill-fortuned invasion of Russia, Sweden took the opportunity to invade and conquer France's ally Denmark, whose fleet had been all but destroyed by the British Navy, and whose army was vastly outclassed by the Swedish army. Although Britain was not enthusiastic about Sweden controlling all of the Baltic, they allowed it for the sake of retaining Sven the Great's allegiances. This began an Anglo-Swedish alliance that has, with a few exceptions, stood until the present.
With the conquest of the Danish kingdom, Sweden also gained nominal control of Norway, Faroe, Iceland, Greenland and the Danish Virgin Islands. While Norway and Denmark were dissolved as political entities and incorporated into the Swedish crown, the other lands were retained as crown colonies. Iceland and Greenland became independent republics in the 1880's, although both still retain their political connections with Sweden.