This book serves as both a primer to astronomical polarimetry and an authoritative overview of its application to various types of astronomical objects from AGN, compact stars, binary systems, stars across the HR diagram, transients, the interstellar medium and solar system bodies. It starts with an historical perspective, a discussion of polarimetric theory, instrumentation and techniques in wave bands from the near infrared to gamma rays. The book presents the state of the art in astronomical polarimetry. It is motivated by the new X-ray polarimeters due to be launched in the next four years and improved optical polarimeters on large telescopes requiring a new analysis of polarimetric theory, methodology and results.This book will be suitable as advanced undergraduate companion text, a primer for graduate students and all researchers with an interest in astronomical polarimetry.