Can you tell me when were the first public libraries appeared in Finland? And where they were built? Thank you.

Public libraries in Finland celebrated their bicentennial in 1994. The founding meeting of the Vaasa Reading Society in the Province of Ostrobothnia on the west coast of Finland took place on the 2nd of August 1794. Although the reading Society was originally meant for its members and partners, other people were also allowed to borrow books for payment. The Reading Society in Vaasa was thus both a "proprietary" and "subscription" library. (Ilkka Mäkinen: Reading Societies in Finland, in Yleiset kirjastot Suomessa. Vaasa 1994, p.104)

The library of the Vaasa Reading Society can be considered to be the beginning of public libraries in Finland. The first public library in Helsinki was founded in 1819, and in Viipuri a public library was opened in 1846. The first library act concerning public libraries was enacted in 1929. (Source: Facta Tietopalvelu encyclopedia.)

So, the date from the 15th century that you found somewhere can definitely not relate to public libraries. The first mentions of scientific libraries known of in Finland relate to the Turku Cathedral library from the 14th century, and the first university library was the Turku Academy library founded in 1640. (Facta Tietopalvelu)