Theory of Distributions 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 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