The author performs a painstaking task of comparison of numerous existing classifications of low-dimensional nilpotent Lie algebras, point out errors in them and put the classification on algorithmic ground: for any given nilpotent Lie algebra of dimension not greater than 6, there is a procedure allowing to identify it with an algebra from the classification list. Moreover, the procedure is implemented in GAP.
The major ingredients of the proof are the Skjelbred-Sund method of constructing nilpotent Lie algebras as central extensions [T. Skjelbred and T. Sund, C. R. Acad. Sci., Paris, Sér. A 286, 241–242 (1978; Zbl 0375.17006)], and identification of Lie algebras by method of Gröbner bases due to the author.