The aim of this book is to provide an advanced introduction to inertial data processing (determination of attitude, velocity and position) along with design architectures and algorithms used to aid the inertial navigation system (INS). The emphasis is on the high-end sensors and systems used in aerospace applications (known as 'navigation grade' or 'nav grade'). The subject of inertial navigation systems and how to aid them (reduce their inherent error drift) is complex and multi-disciplinary. Mathematics and physics along with electrical, mechanical and software engineering all are involved. This book has been written to serve as an introduction for students and those new to the field. Specialized topics such as rotation matrices, quaternions and relevant stochastic processes are covered in the book. The reader is expected to have a basic understanding of vectors, matrices and matrix multiplication as well as freshman-level differential and integral calculus. The basics of inertial position/velocity/attitude updating are first presented with respect to a conceptually simple inertially-fixed reference frame before the impact of the spheroidal rotating earth is covered. Similarly, the key concepts of the Kalman filter are first presented in the context of a scalar filter. Important aspects of the prediction error covariance and Kalman gain equations are thus covered in an intuitive sense before the full matrix formulations are described. By the end of the book, a thorough treatment of modern aided-INS architectures is provided.