Neutron stars are the densest observable bodies in our universe. Born during the gravitational collapse of luminous stars - a birth heralded by spectacular supernova explosions - they open a window on a world where the state of the matter and the strengths of the fields are anything but ordinary. This book is a collection of pedagogical lectures on the theory of neutron stars, and especially their interiors, at the forefront of current research. It addresses graduate students and researchers alike, and should be particularly suitable as a text bridging the gap between standard textbook material and the research literature.