Transformation optics, a recently booming area, provides people a new approach to design optical devices for manipulating light. With transformation optics, a lot of novel optical devices are proposed, such as invisibility cloaks, optical wormholes, optical black holes, illusion devices. The present thesis is devoted to investigate transformation optics for manipulating light. Firstly, an introduction to transformation optics is given. This part includes: (1) introducing differential geometry as the mathematical preparation; (2) expressing Maxwell’s equations in an arbitrary coordinate system and introducing the concept of transformation media as the foundation stone of transformation optics; (3) discussing light from the geometry perspective as the essence of transformation optics; (4) showing how to use transformation optics to design optical devices. For our works on invisibility cloaks, we analyze the properties of arbitrary shaped invisibility cloaks, and confirm their invisibility abilities. The geometrical perturbations to cylindrical and spherical shaped cloaks are analyzed in detail. We show that the cylindrical cloak is more sensitive to the perturbation than a spherical cloak. By imposing a PEC (PMC) layer at the interior boundary of the cylindrical cloak shell for TM (TE) wave, the sensitivity can be reduced dramatically. A simplified non-magnetic cylindrical cloak is also designed. We show that the dominant zeroth order scattering term can be eliminated by employing an air gap between the cloak and the cloaked region. We propose a compensated bilayer by a folding coordinate transformation based on transformation optics. It is pointed out that complementary media, perfect negative index lens and perfect bilayer lens made of indefinite media are well unified under the scope of the transformed compensated bilayer. We demonstrate the applications of the compensated bilayer, such as perfect imaging and optical illusion. Arbitrary shaped compensated bilayers are also analyzed. Nihility media known as the media with ε =μ= 0, are generalized from transformation optics as transformation media derived from volumeless geometrical elements. The practical constructions of nihility media by metamaterials are discussed. The eigen fields in the nihility media are derived. The interactions between an external incident wave and a slab of nihility media in the free space background are analyzed. A new type of transformation media called α media is proposed for manipulating light. Light rays in the α media have a simple displacement or rotation relationship with those in another media (seed media). Such relationship is named α relationship. The α media can be designed and simplified to a certain class of diagonal anisotropic media, which are related to certain isotropic media by the α relationship. Several optical devices based on the α transformation media are designed. Invisibility cloaks obtained from the coordinate transformation approach are revisited from a different perspective. / QC 20101102