  Fundamental duality is a concept which refers to two irreducible,
heterogeneous principles which are in opposite and complementary of each other.
The complementary principle in quantum mechanics is also praised by Bohr. This
important concept is known to appear in a lot of places in our physical
universe, however a rigorous mathematical definition and physics theory has not
yet ever developed in a formal way. In this paper, we establish a formalism for
fundamental duality and study its various properties and theorems. One of the
most profound results is that we establish a relation between dual invariance
and topological invariance, and we find that the topological Chern-Simons form
is a dual invariant action. Finally we apply the concept of duality to study
dual state oscillation, and predict a theoretical new matter of state of
dualiton, which is the particle excitation of the dual field by second
quantization. This new exotic quasi-particle state is expected to have an
impact in particle physics and condensed matter physics.
