This book discusses topics on the Fourier transform, Hankel transform, Weinstein transform, and pseudo-differential operators. Targeted to researchers and graduate students, it is useful in the study of the theory of pseudo-differential operators involving the Weinstein transform. This book is also helpful in the study of partial differential equations, wavelet analysis, harmonic analysis, and functional analysis. Throughout the book, the reader is assumed to have an understanding of the basics of real analysis and functional analysis. The Weinstein transform whose kernel consists of a complex exponential function and a normalized Bessel function of the first kind. The Weinstein transform has a rich calculus and can be applied in many areas of mathematical sciences. Pseudo-differential operators are the generalization of partial differential operators, and they play a significant role in the problems of partial differential equations, numerical analysis, and quantum physics.