Abstract
The purpose of this article is to serve as an introduction to Ulrich bundles for interested readers. We discuss the origins of the study of Ulrich bundles, their elementary properties, and we give an exposition of the known results in their classification on various kinds of smooth projective varieties. As an illustration of a method recently used by Marta Casanellas and Robin Hartshorne for the classification of Ulrich bundles on a cubic surface, we classify the stable Ulrich bundles on a smooth quartic surface in ℙ3 of Picard number 2 by first Chern class.
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