The responsibility for the Swedish national classification system "Klassifikationssystem för svenska bibliotek" (SAB) was passed to Kungliga Biblioteket (KB) 2014 and they ceased to update the system. Instead, KB encourages the Swedish libraries to use the American classification system Dewey decimal classification system (DDC). In a survey from 2016 around 80 % of the Swedish public libraries claim that a shift to DDC is not being planned. This study aims to make a comparative study of these two systems (SAB & DDC) and the new classification system Rainbow which was created in Örnsköldsvik because the librarians who worked there didn’t find either SAB or DDC to be user friendly enough systems. By using a set of concepts the study aims to answer the question what likenesses and differences the three systems have in terms of notation, and to which degree they correspond to the concepts formulated by Batley. By using a comparative system analysis of the notation of the three system the conclusion that SAB fulfills the theoretical framework to 40%, DDC to 40% and Rainbow to 60% where reached.