Vector calculus is a branch of mathematics that focuses on vector fields, which are mathematical constructs that assign a vector to every point in space. It combines concepts from both calculus and linear algebra to analyze and understand how these vector fields behave. Key operations in vector calculus include the gradient, divergence, and curl, which help describe how quantities change in space. This field is essential in various applications, including physics and engineering, where it is used to model phenomena such as fluid flow, electromagnetic fields, and gravitational forces. Understanding vector calculus is crucial for solving complex problems in areas like electromagnetism and mechanics.