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This lecture introduces the concept of algorithms, focusing on their formalization and basic components. It covers the representation of problems as data, the formalization of computations through algorithms, and the illustration of simple problem resolutions. The lecture also discusses the distinction between good and bad sequences of operations, the importance of data structuring, and the independence of algorithms from programming languages. Various control structures like sequences, conditionals, loops, and iterations are explained, emphasizing the need for algorithms to terminate correctly for any input. The lecture concludes by highlighting the challenge of ensuring algorithm correctness for all possible inputs.