Topological states of matter are a rapidly developing area of research in condensed matter physics. Beginning from quantum Hall effect in the 80s-90s, and continuing with topological insulators a decade later, this field of study is now full of theoretical models with anticipated exotic behavior which await their experimental discovery and observation. After a brief introduction into this field, I will describe my work to study topological states of matter with a certain class of topological invariants first proposed in the context of topological insulators and now generalized to include potentially all topological states. I will also discuss the proposed relationship between these invariants and the non-dissipative viscosity, a quantity originally known from the study of plasmas in a magnetic field which more recently received attention in the context of quantum Hall effect.