Shimano Uniglide cassette hub.. I rode on these for years. Good system, and superior to freewheel hubs as explained above.
You'll need to keep the #1 threaded cog to hold everything together; fortunately it doesn't seem too worn. The rest of the cogs can be replaced with far superior shifting Hyperglide (or clone) cassette cogs. Go to your local bike Co-op and find a suitable cassette in which the cogs are loose, or individual cogs are pinned together. $5 at our shop. You may need to do some grinding to remove the pins. Some of the upper-end cassettes are held together with tiny hex-headed pins that look like rivets.
Hyperglide cogs differ from Uniglide in that one (1) of the splines are wider than the rest. A few minutes per cog with a flat file and a bench vice fixes that, until they slide right on. Keep your original spacers.
This way, you have unlimited gearing options, except of course, your necessary #1 cog.