In recent years, artificial materials, metamaterials and plasmonic environments have attracted the attention of the scientific community. The new ideas in these areas offer potential applications in cloaking. In this thesis, after briefly reviewing the available solutions for invisibility and cloaking using metamaterials and plasmonic materials at various frequencies, some of the recently proposed cloaking mechanisms are introduced and this is accompanied by investigating the similarities and differences between different approaches in this regard. The main focus of this thesis is on the design of the invisible cloaks. Various types of these cloaks are proposed based on the transformation optics theory. The focus of this thesis is on the inner invisible cloaks; due to ease and convenience, in all theses, all calculations and simulations have been done in two dimensions. Examples of cylindrical inner cloaks with circular and square sections based on transformation optics are addressed. In one part of this thesis, the design and simulation of the invisible cloak is done using multilayered structures and in another part, this is achieved by using the optical properties of the graphene metamaterial. Invisible structures and the introduced materials do not have some of the disadvantages of the previous models, such as the presence of singularity in structural features and the presence of materials with a negative refractive index; so they are considered suitable for the laboratory construction purposes. Key Words