This is an announcement for the paper "Maps of several variables of finite total variation and Helly-type selection principles" by Vyacheslav V. Chistyakov and Yuliya V. Tretyachenko. Abstract: Given a map from a rectangle in the n-dimensional real Euclidean space into a metric semigroup, we introduce a concept of the total variation, which generalizes a similar concept due to T. H. Hildebrandt (1963) for real functions of two variables and A. S. Leonov (1998) for real functions of n variables, and study its properties. We show that the total variation has many classical properties of Jordan's variation such as the additivity, generalized triangle inequality and sequential lower semicontinuity. We prove two variants of a pointwise selection principle of Helly-type, one of which is as follows: a pointwise precompact sequence of metric semigroup valued maps on the rectangle, whose total variations are uniformly bounded, admits a pointwise convergent subsequence. Archive classification: math.FA Mathematics Subject Classification: 26B30 (Primary); 20M15; 28A20 (Secondary) Remarks: 47 pages, LaTeX, uses elsarticle.sty The source file(s), HSP_arX.tex: 126875 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.0451 or http://arXiv.org/abs/1001.0451 or by email in unzipped form by transmitting an empty message with subject line uget 1001.0451 or in gzipped form by using subject line get 1001.0451 to: math@arXiv.org.