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The topic of this paper is, on the one hand to introduce algebraic analysisresults of \'Etienne B\'ezout (1730- 1783) not as we know them today but as hefound them in his time, and on the other hand to emphasize his innovatingviewpoints. We will be concerned with Bezout special way of reducingelimination for any degree systems to finding conditions for linear systemssolutions, with his typical use of indeterminate coefficients that he doesn'tcompute but looks only for existence and number, with his idea to work on setof polynomials products sums, and with a very personal method to found twoequations resultant.

\'Etienne B\'ezout : Analyse alg\'ebrique au si\`ecle des Lumi\`eres