This work offers detailed coverage of every important aspect of symmetric structures in function of a single real variable, providing a historical perspective, proofs and useful methods for addressing problems. It provides assistance for real analysis problems involving symmetric derivatives, symmetric continuity and local symmetric structure of sets or functions.The Derivative * Continuity * Covering Theorems * Even Properties * Monotonicity * Odd Properties * The Symmetric Derivative * Symmetric Variation * Symmetric Integrals * Problems.