The overall objective of this project is to design and engineering novel types of artificial structures - so called metamaterials, for controlling the propagation of light in an unconventional way, by incorporating topological physics into the metamaterial design. By using metamaterials and metasurfaces as platform, this proposal focuses on the novel topological physics and applications introduced by Berry phase. The flexibility in engineering the artificial ‘atoms’ and ‘molecules’ of metamaterials provides unlimited possibilities to create new structural effect where symmetry (or symmetry breaking) and topology play critical roles. We are particularly interested in the role Berry phase plays in various nontrivial surface optical effects, including topological surface states and spin Hall effect of light. The investigation of the scattering immune surface states in a topological metamaterial, i.e. an effective medium approach, acts to unify the spin Hall effect of light with the more unconventional scheme of topological orders and protected surface states. We will further exploit Berry phase in the nonlinear regime, in particular harmonic generations, to control the nonlinear polarizations to an unprecedented level. Hence our study on Berry phase in the nonlinear regime will point to a new research direction on nonlinearity coefficient engineering, which will have important impact in the area of nonlinear optics. The proposal also investigate into practical applications brought by a novel type of geometrical metasurfaces, where the phase and hence the wavefront are finely controlled by the Berry phase in a highly robust manner. The proposal involves the development of innovative synthesis technologies, theoretical analysis, numerical simulations, experimental characterizations, and device development. The new symmetry and topological effects in this research will greatly impact a number of disciplines including material science, condensed matter physics and photonics. The findings of this project may be applied in various applications such as chemical and bio sensing, medical imaging, optical communications.