“A very readable introduction, which encourages the reader to delve into the subject. … The book is carefully written. It is not an encyclopedia of Riemannian geometry, but a deep introduction to active research topics around the idea of searching good metrics on a manifold. Moreover, it offers a good motivation to these topics, showing the relationship among different classes of Riemannian manifolds.” (Fernando Etayo Gordejuela, zbMATH 1478.53003, 2022)

• Introduction.- Basic Concepts of Riemannian Geometry.- Commutations & Variations.- The Weyl Tensor.- Curvature Conditions.- Critical Metrics of Riemannian Functionals.- Bochner-Weitzenböck Formulas and Applications.- Ricci Solitons: Selected Results.- Existence Results of Canonical Metrics on Four Manifolds.- List of Symbols.- References.- Index.

“A very readable introduction, which encourages the reader to delve into the subject. … The book is carefully written. It is not an encyclopedia of Riemannian geometry, but a deep introduction to active research topics around the idea of searching good metrics on a manifold. Moreover, it offers a good motivation to these topics, showing the relationship among different classes of Riemannian manifolds.” (Fernando Etayo Gordejuela, zbMATH 1478.53003, 2022)

• Introduction.- Basic Concepts of Riemannian Geometry.- Commutations & Variations.- The Weyl Tensor.- Curvature Conditions.- Critical Metrics of Riemannian Functionals.- Bochner-Weitzenböck Formulas and Applications.- Ricci Solitons: Selected Results.- Existence Results of Canonical Metrics on Four Manifolds.- List of Symbols.- References.- Index.