This book is a collection of articles from the Special Issue "Inequalities" published in the open-access journal *Mathematics* (ISSN 2227-7390) from 2018 to 2019. The articles were peer-reviewed and published by Shigeru Furuichi, the Special Issue Editor, and are distributed under the Creative Commons Attribution (CC BY) license. The book covers a wide range of topics in mathematical inequalities, including coefficient inequalities for functions associated with petal type and hyperbolic domains, inequalities for g-frames in Hilbert C*-modules, Gronwall-Bellman inequalities in frame of generalized proportional fractional derivative, Hermite-Hadamard inequalities for interval (h1, h2)-convex functions, and more. The articles provide new and interesting results in the field of mathematical inequalities, offering insights into the latest developments and refinements in the area.This book is a collection of articles from the Special Issue "Inequalities" published in the open-access journal *Mathematics* (ISSN 2227-7390) from 2018 to 2019. The articles were peer-reviewed and published by Shigeru Furuichi, the Special Issue Editor, and are distributed under the Creative Commons Attribution (CC BY) license. The book covers a wide range of topics in mathematical inequalities, including coefficient inequalities for functions associated with petal type and hyperbolic domains, inequalities for g-frames in Hilbert C*-modules, Gronwall-Bellman inequalities in frame of generalized proportional fractional derivative, Hermite-Hadamard inequalities for interval (h1, h2)-convex functions, and more. The articles provide new and interesting results in the field of mathematical inequalities, offering insights into the latest developments and refinements in the area.