The research field of metamaterials is rapidly advancing. In particular, the most recent developments on transformation optics and metasurfaces are exploiting the usage of inhomogeneous metamaterials in controlling light. However, to date, there is no single introductory book available for students or newcomers to this interdisciplinary field to systematically study the basic ideas and concepts. Including practical guidance, this book will allow those new to the field, in particular those interested in using inhomogeneous metamaterials for designing optical components, to immediately commence working in this exciting research area. Written at a level approachable by graduate students and senior-year undergraduate students, majoring in physics, engineering or materials science, this book will provide an introduction to the two most prevalent approaches in this subject: transformation optics and metasurfaces. The authors include full mathematical details of the background theories and concentrate on the important examples, from theory, practical design with procedures and a brief introduction to experimental realizations. In order to carry out the numerous examples in the book, it comes with full-wave simulation code.