Tensor calculus is a mathematical framework that extends traditional calculus to higher-dimensional spaces using objects called tensors. Tensors can be thought of as multi-dimensional arrays that generalize scalars, vectors, and matrices, allowing for the representation of complex relationships in physics and engineering. This branch of mathematics is particularly useful in fields like general relativity, where it helps describe the curvature of space-time, and in continuum mechanics, where it models stress and strain in materials. Tensor calculus provides the tools to perform operations like differentiation and integration on these multi-dimensional entities, facilitating the analysis of complex systems.