Sweden has a long history of providing courses at various levels for interested students. There are folk high schools, adult education schools and vocational studies, to name a few. Municipalities offer a course called Swedish for Immigrants (SFI) for newly arrived individuals. In most cases, however, the individual must have a resident permit in order to begin their studies.
It can be good to read up on the various options available to you so that you're prepared when you've received your resident permit. You can find more information right here on Studera.nu.
Options for learning Swedish
There are various organisations that provide support to asylum-seekers. Some can help with for example classes in Swedish. The Swedish Migration Agency has a list of links to these organisations. Here is a link to their website where you can find information in various languages about seeking asylum in Sweden, and links to various help organisations:
Swedish Migration Agency's information to asylum-seekers
Page last updated 2016-02-10