What are the relations between the notation in Lusztig's book introduction to quantum groups and the usual notation about quantum groups. For example, $v$ in Lusztig's book corresponds to the usual $q$. Are $E, F, K$ in Lusztig's book the same as the usual ones? I think ${}^{'}U$ and $U$ are quantum groups. What are the algebras ${}^{'}{\bf f}$ and ${\bf f}$ used for? What are the relations between $f$ and $U$? Thank you.