Radar imaging is a mathematically-rich subject with many interesting applications and a large variety of challenging, mathematical open problems. The goal of this book is to provide mathematicians with the background they need to work in the field, building on the foundation of the underlying partial differential equations. The focus is on showing the connection between the physics and the mathematics and on supplying an intuitive mathematical understanding of basic concepts. The book includes a description of how a radar system works, together with the relevant mathematics; theory that guides the choice of radar waveforms; derivation of the fundamentals of scattering theory; derivation and discussion of the image formation process; and a long list of current open problems. Applied mathematicians will want this book because it explains the basics of radar imaging, provides a foundation for understanding the engineering literature, and gives references for many of the open problems.