Chapter 1. Introduction -- Chapter 2. Characterization of hydrometeors -- Chapter 3. Wave scattering by a single particle -- Chapter 4. Scattering and propagation in clouds and precipitation -- Chapter 5. Radar measurements and improvement of data quality -- Chapter 6. Applications in weather observation and quantification -- Chapter 7. Advanced methods and optimal retrievals -- Chapter 8. Phased array radar polarimetry.;This book presents the fundamentals of polarimetric radar remote sensing through understanding wave scattering and propagation in geophysical media filled with hydrometers and other objects. The text characterizes the physical, statistical, and electromagnetic properties of hydrometers and establishes the relations between radar observables and physical state parameters. It introduces advanced remote sensing techniques (such as polarimetric phased array radar) and retrieval methods for physical parameters. The book also illustrates applications of polarimetric radar measurements in hydrometer classification, particle size distribution retrievals, microphysical parameterization, and weather quantification and forecast.