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Synopsis The present Learned Research Work is an exhaustive survey and researches carried out by the authors, which led to the theories of distributions, generalized functions and transforms involving them, which includes interesting results and the fundamental concepts of the youngest generalization of Schwartz theory of distribution, the Boehmians. The tempered distribution and ultradistributions have been described, which provide suitable platforms for the generalizations of Fourier transforms, Stieltjes and Mellin transforms. To overcome the Fourier series, this work includes wavelet transform, for which meticulous extensive study of the existing literature has been produced including recent researches carried out by the authors. This compilation, in the form of the present book, is believed to be of help to researchers in the field of distribution and transform analysis and, may even be treated as the reference book to post graduate students.