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From time to time a new algorithm comes along that causes a sensation in theoretical computer science or in an area of application because of its resolution of a long-standing open question, its surprising efficiency, the novelty of its setting or approach, the elegance of its structure, the subtlety of its analysis or its range of applications. We will present a variety of such algorithms, mostly drawn from the following list, in the chronological order of their appearance. Elementary examples: Binary arithmetic, Euclidean algorithm, greedy algorithm, Dijkstra shortest-path algorithm, Gaussian elimination, bipartite matching.