Let \(U_ q\) denote the quantized enveloping algebra over \({\mathbb{Q}}(q)\) associated to a symmetrizable Kac-Moody algebra \({\mathfrak g}\). For any integrable \(U_ q\)-module M the author defines a crystal base for M to be a pair (L,B) consisting of a lattice L of M and a \({\mathbb{Q}}\)-basis B of L/qL with certain nice properties. In the paper under review the author proves the existence and uniqueness of crystal bases for the case where \({\mathfrak g}\) is a finite dimensional classical Lie algebra, and in the paper reviewed above he announces the extension to the general case [see also Preprint 728, Res. Inst. Math. Sci., Kyoto Univ. for details and proofs)]. \textit{G. Lusztig} has constructed a so-called canonical basis for the \(+\) part of \(U_ q\) (for types A, D and E), see [J. Am. Math. Soc. 3, 447- 498 (1990; Zbl 0703.17008) and Prog. Theor. Phys. Suppl. 102, 175-201 (1990)]. On the irreducible integrable highest weight modules the two constructions lead to the same bases.