The detection of gravitational waves has ushered in a new era of gravitational wave astronomy and added a new medium to multi-messenger astronomy. This book examines the theoretical foundation of gravitational waves and the state of the art of gravitational wave detection including interferometric detectors and pulsar timing arrays. The design and sensitivity of the LIGO interferometers are examined. The source and data analysis method for each of the four main classes of gravitational waves (compact binary coalescence, burst, continuous, and stochastic) are described. A summary of the gravitational waves that have been detected as of January 2019 is presented along with what gravitational wave astronomy has been extracted from these observations. Finally, what the future of gravitational wave exploration looks like in terms of ground-based and space-based detectors is presented.