This course provides a foundational introduction to vector calculus, focusing on vector-valued functions of a single variable. You will master the rules for differentiating and integrating vectors, and learn how these operations relate to the geometry of parametric curves. The curriculum is built to give you a solid understanding of the mathematical tools that describe change in multiple dimensions. How do we precisely describe the motion of a satellite or a particle moving along a curved path? This course answers that question by bridging the gap between abstract calculus and the real-world physics of motion. You'll learn how the elegant tools of vector differentiation and integration allow us to model velocity, acceleration, and trajectories, providing the essential language for kinematics. This course is the essential next step for students who have a firm grasp of vector algebra and products. It is specifically designed for first-year university students in STEM fields who need to understand the calculus of vectors before tackling more advanced courses. This programme provides the critical foundation for future studies in vector mechanics, differential geometry, and the calculus of vector fields.