Written by experts in the field, this text provides a modern introduction to three-dimensional dynamics for multibody systems. It covers rotation matrices, the twist-wrench formalism for multibody dynamics and Lagrangian dynamics, an approach that is often overlooked at the undergraduate level. The only prerequisites are differential equations and linear algebra as covered in a first-year engineering mathematics course. The text focuses on obtaining and understanding the equations of motion, featuring a rich set of examples and exercises that are drawn from real-world scenarios. Readers develop a reliable physical intuition that can then be used to apply dynamic analysis software tools, and to develop simplified approximate models. With this foundation, they will be able to confidently use the equations of motion in a variety of applications, ranging from simulation and design to motion planning and control.