This is from 2003 (December, so it's about 21 years ago). Is it still relevant?
It's the only edition which is provided for free. This edition uses Lua 5.0, which is very similar to 5.1 which is still very popular as it's targeted by LuaJIT. The changes between 5.1 and 5.2 seem small as well.
Yes. The differences between 5.0 and 5.1 are small and I do not recommend using newer versions, regardless.