We invent the notion of a {\it dimension of a variety} V as the cardinality
of all its proper {\it derived} subvarieties (of the same type). The dimensions
of varieties of lattices, varieties of regular bands and other general
algebraic structures are determined.Comment: The results of the paper were presented at the workshop AAA71 and
CYA21 at B\c{e}dlewo, Poland on February 11, 2006. the paper is submitted to
Discussiones Mathematicae Algebra and Stochastc Methods, special issu
