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These notes give an introduction to the physics of the infinite range versionof the Edwards--Anderson model, the so-called Sherrington--Kirkpatrick model.In a first part, I motivate and introduce the Edwards--Anderson andSherrington--Kirkpatrick models. In the second part, I explain the analyticalsolution of the Sherrington--Kirkpatrick model, following Giorgio Parisi. Inext give the physical interpretation of this solution. This is a vast subject,and I concentrate on the major points and give references for more details. Thethird part presents the simulation approach and compare its results totheoretical expectations: thermodynamics, finite size scaling, determination ofthe critical temperature using "parameters" like the "Binder parameter", andfluctuations. The last part gives a summary of our current understanding offinite size effects for the free energy and internal energy of theSherrington--Kirkpatrick model

Some aspects of infinite range models of spin glasses: theory and numerical simulations