The objective of the present paper is to provide a simple approach to statistical inference using the method of transformations of variables. We demonstrate performance of this powerful tool on examples of constructions of various estimation procedures, hypothesis testing, Bayes analysis and statistical inference for the stress-strength systems. We argue that the tool of transformations not only should be used more widely in statistical research but should become a routine part of calculus-based courses of statistics. Finally, we provide sample problems for such a course as well as possible undergraduate research projects which utilize transformations of variables. (Contains 1 table.)