I'm interested in learning about the classification system used in your library
You do not specify the library whose classification system you would like to know about. Do you mean the classification systems in Finnish libraries in general?
There are several classification systems used in different libraries in Finland. First of all, to get a general idea about the Finnish library system, please have a look at http://www.libraries.fi/en-GB/ , where you will find access to basically every library in Finland, along with their web OPACs (open public access catalogues).
Roughly, one could say that the public libraries here use the Finnish Public Libraries Classification System (PLC) and the scientific and university libraries use the Universal Decimal Classification (UDC). This would nevertheless give an oversimplified idea, because many of our libraries have made applications of their own of these systems.
UDC, of course, is an international system, so you are probably acquainted with that, but if not, please look e.g. at http://www.udcc.org/about.htm
You will find the English version of the Finnish Public Libraries Classification System at http://ykl.kirjastot.fi/index.aspx .
I myself work at Helsinki City Library, and here we have a classification system of our own. After all, it is an application of the good old Dewey decimal system, but there is no other library in the world using exactly the same system as we do. If you would like to go into the depths of our system, please look at http://hklj.kirjastot.fi/.
Helsinki City Library is working in a consortium together with the neighbouring cities Espoo, Kauniainen and Vantaa, who then again use the PLC with only minor exceptions. Nevertheless, in our web library ( http://www.helmet.fi/search~S9/X ) you will see that there are separate classification searches for each of these four individual cities (path: Other searches -> Select search).