The author extends results on Hölder conditions of the sample paths and the Hausdorff dimension of the image, graph and level sets previously known for Gaussian fields to stable fields. A concept analogous to an index-\(\beta\) Gaussian field is defined for stable fields. Under this condition and an extra regularity condition, results paralleling those for the Gausian case are given. The regularity condition is needed to establish the Hölder condition and examples are given to show it cannot be deleted.