Numerical libraries are collections of pre-written code that provide tools for performing mathematical calculations and data analysis. They are designed to simplify complex operations, such as linear algebra, statistical analysis, and numerical optimization. These libraries are widely used in programming languages like Python, R, and C++ to enhance computational efficiency and accuracy. Common examples of numerical libraries include NumPy and SciPy for Python, which offer functions for array manipulation and scientific computing. By using these libraries, developers can save time and reduce errors, allowing them to focus on solving problems rather than writing code from scratch.