In a 1971 article, Japanese mathematician Atsushi Inoue introduced a locally C* algebra, which is a fairly broad generalization of a C* algebra. Many objects and theorems of a C* algebra have appropriate generalizations in a locally C* algebra, e.g. positive elements, Gelfand Theorem and Gelfand Naimark Theorem. It turns out that, these generalizations have interpretations and applications in physics, similar to a C* algebra. In this talk, we review various properties of a locally C* algebra, and discuss how they generalize the corresponding properties of a C* algebra.