I resolved using the library. It resulted to be quite easy to work with the classes provided:
First I had to create a WlanClient object
wlan = new WlanClient();
And then I can get the list of the SSIDs the PC is connected to with this code:
Collection<String> connectedSsids = new Collection<string>();
foreach (WlanClient.WlanInterface wlanInterface in wlan.Interfaces)
{
Wlan.Dot11Ssid ssid = wlanInterface.CurrentConnection.wlanAssociationAttributes.dot11Ssid;
connectedSsids.Add(new String(Encoding.ASCII.GetChars(ssid.SSID,0, (int)ssid.SSIDLength)));
}