This issue of the Reference Mathematical Library series focuses on integral transformations and operational calculus. The first part sets out the foundations of the theory of integral transformations of Fourier, Laplace, Mellin, Bessel, Hankel, Meyer, Kantorovich - Lebedev, etc. Particular attention is paid to the Laplace transform and its application to mathematical analysis. Operational calculus is presented on the basis of Mikusinsky's theory with some modification of it.