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The theory of time scales was introduced by Stefan Hilger in his PhD thesis in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized.