Equivariant Formality for Actions of Torus Groups This paper contains a comparison of several definitions of equivariant formality for actions of torus groups. We develop and prove some relations between the definitions. Focusing on the case of the circle group, we use $S^1$-equivariant minimal models to give a number of examples of $S^1$-spaces illustrating the properties of the various definitions. Keywords:Equivariant homotopy, circle action, minimal model,, rationalization, formalityCategories:55P91, 55P62, 55R35, 55S45