Complex sentence: Traffic on Tvärbanan started in 2000 first between Gullmarsplan and Liljeholmen, then later between Liljeholmen and Alvik and in 2002 between Gullmarsplan and Sickla udde.
Split into simpler sentences: Traffic on Tvärbanan started in 2000 first between Gullmarsplan and Liljeholmen, then a bit later between Liljeholmen and Alvik. And in 2002 between Gullmarsplan and Sickla udde.