Peter B. Gilkey is a Professor of Mathematics and a member of the Institute of Theoretical Science at the University of Oregon. He is a fellow of the American Mathematical Society and is a member of the editorial board of Results in Mathematics, J. Differential Geometry and Applications, and J. Geometric Analysis. He received his Ph.D. in 1972 from Harvard University under the direction of of L. Nirenberg. His research specialties are Differential Geometry, Elliptic Partial Differential Equations, and Algebraic topology. He has published more than 250 research articles and books.Jeong Hyeong Park is a Professor of Mathematics at Sungkyunkwan University and is an associate member of the KIAS Korea). She received her Ph.D. in 1990 from Kanazawa University in Japan under the direction of H. Kitahara. Her research specialties are spectral geometry of Riemannian submersion and geometric structures on manifolds like eta-Einstein manifolds and H-contact manifolds. She organized the geometry section of AMC 2013 (The Asian Mathematical Conference 2013) and the ICM 2014 satellite conference on Geometric analysis. She has published more than 71 research articles and books.Ramon Vazquez-Lorenzo is a member of the research group in Riemannian Geometry at the Department of Geometry and Topology of the University of Santiago de Compostela (Spain). He is a member of the Spanish Research Network on Relativity and Gravitation. He received his Ph.D. in 1997 from the University of Santiago de Compostela under the direction of E. Garcia-Rio. His research focuses mainly on Differential Geometry with special emphasis on the study of the curvature and the algebraic properties of curvature operators in the Lorentzian and in the higher signature settings. He has published more than 50 research articles and books.

Preface.- Acknowledgments.- Basic Notions and Concepts.- Manifolds.- Riemannian and Pseudo-Riemannian Geometry.- Bibliography.- Authors' Biographies.- Index .