The chapter provides an overview of the book "Mathematical Aspects of Discontinuous Galerkin Methods" by Daniele Antonio Di Pietro and Alexandre Ern. The book aims to introduce readers to the fundamental mathematical concepts and techniques used in designing and analyzing discontinuous Galerkin (dG) methods for various model problems. It covers both linear and nonlinear PDEs, focusing on scalar first-order, second-order, and systems of PDEs. Key topics include well-posedness, mesh refinement, numerical fluxes, discrete gradients, and error estimates. The book also discusses practical implementation aspects and includes a comprehensive bibliography. The intended audience is graduate students and researchers in applied mathematics and numerical analysis, as well as those in engineering sciences interested in the mathematical foundations of dG methods.The chapter provides an overview of the book "Mathematical Aspects of Discontinuous Galerkin Methods" by Daniele Antonio Di Pietro and Alexandre Ern. The book aims to introduce readers to the fundamental mathematical concepts and techniques used in designing and analyzing discontinuous Galerkin (dG) methods for various model problems. It covers both linear and nonlinear PDEs, focusing on scalar first-order, second-order, and systems of PDEs. Key topics include well-posedness, mesh refinement, numerical fluxes, discrete gradients, and error estimates. The book also discusses practical implementation aspects and includes a comprehensive bibliography. The intended audience is graduate students and researchers in applied mathematics and numerical analysis, as well as those in engineering sciences interested in the mathematical foundations of dG methods.