Coq is an interactive theorem prover that allows users to write mathematical definitions, executable algorithms, and theorems, and then formally verify their correctness. It is based on a formal language that supports both functional programming and logical reasoning, making it a powerful tool for mathematicians and computer scientists. Developed in the 1980s, Coq is widely used in academia and industry for formal verification of software and hardware systems. Its rich ecosystem includes libraries for various domains, enabling users to build complex proofs and ensure the reliability of critical systems through rigorous verification processes.