Formal methods are mathematical techniques used in computer science and engineering to specify, develop, and verify software and hardware systems. They provide a rigorous framework for ensuring that systems behave as intended, helping to identify and eliminate errors early in the development process. These methods often involve creating formal specifications, which are precise descriptions of system behavior, and using tools to prove that the implementation meets these specifications. Common applications include safety-critical systems in industries like aerospace and automotive, where reliability is essential. Examples of formal methods include model checking and theorem proving.