This book focuses on various aspects of combinatorial mathematics, with a specific emphasis on graph theory and discrete geometry. It covers recent advances in global optimization for combinatorial discrete problems, exploring topics such as three-way combinatorial identity, logical models of combinatorial problems, variants of the Riemann Zeta function, summation formulae for quintic q-series, combinatorial enumeration of graphs, combinatorial preon models for matter and unification, the Newton-Puiseux algorithm and triple points for plane curves, asymptotic properties of random restricted partitions, locally balanced G-designs, generating functions for four classes of triple binomial sums, and an exact approach for selecting pickup-delivery stations in urban areas to reduce distribution emission costs.The book will be of beneficial to mathematicians, researchers, and students specializing in combinatorial mathematics, graph theory, and discrete geometry. It would also appeal to professionals and academics working in fields related to optimization, algorithms, and mathematical modeling.