The chapter introduces the book "Geometry and Spectra of Compact Riemann Surfaces" by Peter Buser, which is part of the Modern Birkhäuser Classics series. The book is a reprint of the 1992 edition and covers two main subjects: the geometric theory of compact Riemann surfaces and the Laplace operator and its relationship with the geometry of these surfaces. The content is divided into two parts: the first part focuses on the geometry of compact Riemann surfaces using hyperbolic geometry and cutting and pasting techniques, while the second part delves into the spectrum of the Laplace operator and its connection to the geometry of these surfaces. The book includes detailed proofs and new results, making it a valuable resource for graduate students and researchers in mathematics.The chapter introduces the book "Geometry and Spectra of Compact Riemann Surfaces" by Peter Buser, which is part of the Modern Birkhäuser Classics series. The book is a reprint of the 1992 edition and covers two main subjects: the geometric theory of compact Riemann surfaces and the Laplace operator and its relationship with the geometry of these surfaces. The content is divided into two parts: the first part focuses on the geometry of compact Riemann surfaces using hyperbolic geometry and cutting and pasting techniques, while the second part delves into the spectrum of the Laplace operator and its connection to the geometry of these surfaces. The book includes detailed proofs and new results, making it a valuable resource for graduate students and researchers in mathematics.