Abstract: This comprehensive summary systematically organizes and presents conventions, notations, abbreviations, glossary, and references essential for understanding and navigating the technicalities and terminologies in extensive mathematical studies. As a fundamental resource, it offers clarity to the complexities inherent in mathematical communication and expression. This preprint version, open for peer review, invites discussion and feedback within the scientific community to further refine approaches and conclusions.This study, presented as a preprint, offers preliminary insights that are yet to undergo peer review. Future revisions may further refine the findings and conclusions drawn here. Keywords: Mathematical Notations, Polynomial Sequences, Real Number Line Representation, Cartesian Plane Axes, Symbolic Mathematics, Integer Sequences, Mathematical Glossary, Mathematical Lexicon, Non-Standard Notations, Mathematical Conventions. 2020 Mathematics Subject Classification: 00Axx: General and miscellaneous specific topics, 03Gxx: Algebraic logic and universal algebra, 05Axx: Enumerative combinatorics, 11Bxx: Sequences and sets, 12Yxx: Computational aspects of field theory and polynomials, 14Qxx: Computational aspects in algebraic geometry, 97-xx: Mathematics education.