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We describe the context where p-adic numbers were created at the end of the nineteenth century. Next, algebraic and topologic structures were constructed on that set of numbers by K. Hensel. They are the only complete valued extensions of Q, different from R. All non-Archimedean mathematics grew up during the twentieth century where the fields Qp play the role of R. Now, p-adic analysis finds applications in various scientific domains: quantum physic, dynamical systems, computers. The paper insists on the analogies and overall the differences between methods and results obtained in classical and non-Archimedean mathematics.

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