General relativity and gravitational waves : essentials of theory and practice Preface 1 Special Relativity 2 Equivalence Principle 3 Tensor algebra in curvilinear coordinates 4 The Geometry of Curved Spaces and Tensor Calculus 5 Einstein’s Equations 6 Schwarzschild Solution and Black Holes 7 Tests of GR 8 Gravitational Waves 9 GW Data Analysis Bibliography. This book serves as a textbook for senior undergraduate students who are learning the subject of general relativity and gravitational waves for the first time. Both authors have been teaching the course in various forms for a few decades and have designed the book as a one stop book at basic level including derivations and exercises. A spectacular prediction of general relativity is gravitational waves. Gravitational waves were first detected by the LIGO detectors in 2015 hundred years after their prediction. Both authors are part of the LIGO Science Collaboration and were authors on the discovery paper. Therefore a strong motivation for this book is to provide the essential concepts of general relativity theory and gravitational waves with their modern applications to students and to researchers who are new to the multi disciplinary field of gravitational wave astronomy. One of the advanced topics covered in this book is the fundamentals of gravitational wave data analysis filling a gap in textbooks on general relativity. The topic blends smoothly with other chapters in the book not only because of the common area of research but it uses similar differential geometric and algebraic tools that are used in general relativity.