Abstarct: Quantum algebras have been receiving much attention in physics and mathematics in the past four decades. In this dissertation, we investigated the deformed formalism. We know, deformed formalism is general form than its corresponding initial theory. So that, in the limited case of deformed parameter, the initially formalism is recover. Such as, Newton mechanics is a special case of relativistic mechanics that deformed parameter is β=V/C and when β→0 the well-know Newton mechanics is recover. as well as, quantum mechanics is generalize Classical mechanics and deformed parameter is 1/h in quantum mechanics, when 1/h → ∞ ,quantum mechanics change to Classical mechanics. It is now, assumed the deformed theories are obtained by introducing a dimensionless deformed parameter into one of the fundamental relations of initially theories. The structure of this dissertation is as follows: first, we introduced a deformed formalism. Then, we studied deformed Heisenberg - Weil algebra and the q-deformed trigonometric function. The deformed complex number and its conjugate is also investigated. In addition to, we discussed the creation and annihilation operators in this deformed formalism according to the creation and annihilation operators in ordinary quantum space. Then, by using of the deformed formalism, deformed Quantum and Classical harmonic oscillator are investigated. The free particle behavior in this space is similar to the particle with charge which moving in ordinary space in the presence of magnetic field. In each section, we introduce the deformed quantum and classical Hamiltonians and we obtain the energy spectrum. Then, at each step of these steps, the results Compare with result of the corresponding initially theories. In next section, we investigated statistical mechanics in deformed formalism which we will call superstatistics. In the limited case, superstatistics reduce to the Boltzmann factor of ordinary statistical mechanics. By using of this descxription, we studied relativistic and non-relativistic systems in the deformed formalism. As well as, we discussed the temperature fluctuation instead of the inverse temperature fluctuation in the superstatistics. Then, the relativistic scattering problem in deformed version of Dirac equation is derived. in addition to, we studied the applications of deformed formalism in nuclear physics. Also, we investigated the nuclear models, which including the Nilsson model and the Interacting bosons model. In addition to, we studied the Interacting bosons model in deformed formalism. With removed the deformed parameter, a good agreement between the deformed formalism and ordinary formalism is found. Finally, our conclusion is appeared in last section.