This book is intended for students and researchers in STEM as a reference to the Mellin transform. It exploits the advantage of using the Mellin transform, potentially turning a second order linear differential equation into a first order linear difference equation, which is solvable by iteration. This is applied exclusively to Schrödinger's equation in this book. This method is actually more powerful than the Laplace transform method, as it leads to a solution for any solvable potential model. For the case of unsolvable potentials, the Mellin transform turns Schrödinger's equation into a higher order difference equation or a differential-difference equation which cannot be solved by iteration; these cases will not be discussed in this book. Some mathematical rigour is removed to make the material more accessible.