This book aims to present some analytic inequalities and their applications in partial differential equations. These inequalities include integral inequalities, differential inequalities and difference inequalities which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. The material summarizes a vast literature such as published papers, preprints and books in which inequalities are categorized in terms of different properties which are consequences of those inequalities such as (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions for some partial differential equations.