Les �quations polynomiales apparaissent dans de nombreux domaines, pour mod�liser des contraintes g�om�triques, des relations entre des grandeurs physiques, ou encore des propri�t�s satisfaites par certaines inconnues. Cet ouvrage est une introduction aux m�thodes alg�briques permettant de r�soudre ce type d'�quations. Nous montrons comment la g�om�trie des vari�t�s alg�briques d�finies par ces �quations, leur dimension, leur degr�, ou leurs composantes peuvent se d�duire des propri�t�s des alg�bres quotients correspondantes. Nous abordons pour cela des m�thodes de la g�om�trie alg�brique effective, telles que les bases de Grobner, la r�solution par valeurs et vecteurs propres, les r�sultants, les bezoutiens, la dualit�, les alg�bres de Gorenstein et les r�sidus alg�briques. Ces m�thodes sont accompagn�es d'algorithmes, d'exemples et d'exercices, illustrant leurs applications.

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