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This book is unique in its emphasis on developing fundamentals of Galilean mechanics, under the conditions rejecting discreteness of 'analytic' mechanics, rejecting presence of rotating and deformation particles in locally continuous media. The main properties of Galilean mechanics universe are formulated as axioms of density balance for 6-- dimensional bi-vector measures (screws). This leads to the principally new architecture of Galilean mechanics as geometry of generalized Galilean group. Audience: graduate students and researchers in the field of mathematics and mechanics.