This book is devoted to new advances in all branches of mathematics, game theory and applications, and pure and applied algebra and geometry including Field Theory and Polynomials, Commutative Rings and Algebras, Algebraic Geometry, Linear and Multi-linear Algebras, Matrix Theory, Associative Rings and Algebras, Nonassociative Rings and Algebras, K-Theory, Group Theory and Generalisations, Topological Groups, Lie Groups, Geometry, Differential Geometry.