The Journal of SYMMETRY welcomes submissions to the special issue on the Advances in Number Theory and their Applications '. In addition to selected contributions high-quality papers that outline recent progress in the theory of Advances in Number Theory and their Applications. Therefore, the selected (and duly-refereed) papers will be published in this Special Issue. This Special Issue will focus on the recent advances in Pure & Applied Mathematics and related areas. Potential topics include, but are not limited to the following topics: Algebra and Analytic Number Theory Special numbers and Special functions Geometry and Its Applications Combinatorics and Probability Polynomials and Orthogonal systems Q-theory and Its Applications Pure and Applied Mathematics & Statistics Mathematical Analysis Mathematical Physics Fractional Calculus and Its Applications Approximation Theory and Optimization Extremal problems and Inequalities Integral Transformations, Equations and Operational Calculus Partial Differential Equations Mathematical Methods and Computation in Engineering