This is a revised edition of the chapter on Complex Variables, which was published few years ago in Part II of My Personal Study Notes in Advanced Mathematics. In this edition, I reproduced, refined, and enhanced all the calculations and graphics in a modern style of representation. In addition, I re-typed the cursive scripts of the personal notes and edited the typographic errors. In the editing process, I added plenty of comments on the underlying meanings of the arcane equations, such that the reader could discern the practical weight of each mathematical formula. In a way, I attempted to...