Textbook in PDF format This book offers an introduction to Newton–Cartan gravity, a reformulation of Newtonian gravity in differential-geometric language, which brings it closer to General Relativity (GR) than the standard formulation. The text systematically develops Newton–Cartan gravity from its geometric foundations, and provides a detailed discussion of the classical results on its relation to both standard Newtonian gravity and GR. Furthermore, it presents a global formulation of the gauge- theoretic perspective that underlies many modern developments in this field, and briefly discusses applications in Newtonian limits of string theory. This book is designed for researchers and graduate students in gravitational physics and related disciplines, providing a clear path toward understanding current research literature