Gorenstein algebras are higher dimensional analogs of self-injective algebras, e.g. the integral group ring $\mathbb{Z} G$ vs the group algebra $\mathbb{C} G$ of a finite group. Their representations of interests are the lattices, or the maximal Cohen-Macaulay (MCM) modules, which satisfy a cohomological vanishing property vacuous for self-injective algebras. The stable category of MCM modules, obtained by factoring out morphisms factoring through projective modules, is always triangulated. This talk is meant as an introduction to the structure of this category, focusing on cases arising from curve and surface singularities where complete classifications of indecomposables can be obtained by quiver theoretic methods.