The most up-to-date public transport maps for Reykjavik and the the rest of Iceland are found on the local bus company’s website. They include route maps for the whole of Iceland, the capital area and a night bus map. If you want a pdf version of one of them, just click it to download. The map below is a clickable direct link to the capital area network map
When you’ve figured out which bus line you want, you can find timetables for each line on this Icelandic bus company’s timetable page. Current schedules for Reykjavik city buses, including night buses, are there, as well as the timetables for buses covering the rest of Iceland.