Lt. Hija said:

Now that someone has mentioned it, can somebody explain to me what work of Vader Kylo intends "to finish"?

Vader's last work - we witnessed - was to get rid of the Emperor and convert back to the bright side of the Force...?!?

I've been wondering the same thing. In the ROTS, wasn't his work to eliminate all the Jedi and to become the most powerful? Maybe Kylo doesn't want not even one Jedi (Luke) around. Kylo does seem pretty powerful so I'm curious to know where he learned all this. Self taught dark lord?

Also, why didn't Luke train Leia to become a Jedi since she is technically a Skywalker? Maybe she refused and decided it was better to become a General.