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This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

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1 Introduction.- 2 Generalities on distributions.- 3 Differentiation.- 4 Homogeneous distributions.- 5 Direct product of distributions.- 6 Convolutions.- 7 Tempered distributions.- 8 Integral transforms.- 9 Fundamental solutions.- 10 Sobolev spaces.

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"Uniquely, this work by Georgiev (Univ. of Sofia, Bulgaria) reads stylistically like a brief, basic, but exotic calculus text, replete with concrete sample calculations. Many researchers found distributions quite alien when they made the scene 65 years ago, but with this book, today´s mathematics and physics undergraduate students may well come to regard them as quite routine. Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners." (D. V. Feldman, Choice, Vol. 53 (10), June, 2016)

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Prof. Svetlin G. Georgiev , Assistant Professor, Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia "St. Kliment Ohridski", Sofia, Bulgaria.

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