Z-Transform is one of several transforms that are essential mathematical tools used in engineering and applied sciences. This short edition of this note is written to provide an introduction to the subject of Z-Transform. The material presented in this note can be covered in four to five 2-hour classroom lectures. Basic knowledge of calculus is needed. The note is not intended as a substitute for a text book on the subject. It is intended to help readers and students in engineering, mathematics and applied sciences understand the basic properties of Z-Transform and some of the methods and techniques based on this transform to solve some engineering and science problems. I have collected many examples and problems on the subject that might help the reader getting on-hand experience with the techniques presented in this note.