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After a brief summary of the foundations of general relativity, we willconcentrate on the stationary exact solutions of the Einstein andEinstein-Maxwell equations. A number of these solutions can be interpreted asblack holes, corresponding to a special spacetime geometry. Then, we will showthat the reformulation of the stationary Einstein-Maxwell equations as agravitating sigma model provides us with a powerful tool to generate newsolutions.

Relativit\'e g\'en\'erale: solutions exactes stationnaires