Non-linear optical phenomena have been widely investigated and well understood since the invention of the Laser. Lots of applications of the non-linear optical phenomena have always been advanced in various fields, such as, optical information storage, all-light computing, optical switch, optical limiters, micro-nano-fabrication, etc., Non-linear optics has been developed into a subfield of optics, and there is no indication that either the developments of non-linear optics or its applications are slowing down. In non-linear optics, the characterisation and measurement techniques of the non-linear index are critical for understanding the non-linear physical process and developing new applications. In this book, different optical non-linearity characterisation and measurement methods are introduced and non-linear problems are discussed theoretically. This book is invaluable to advanced undergraduates, graduate students and researchers working in the fields of physics, materials, and chemistry.