This thesis compares the performance and robustness of five different varities of discriminant analysis, namely linear (LDA), quadratic (QDA), generalized quadratic (GQDA), diagonal linear (DLDA) and diagonal quadratic (DQDA) discriminant analysis, under elliptical distributions and small sample sizes.  By means of simulations, the performance of the classifiers are compared against separation of mean vectors, sample size, number of variables, degree of non-normality and covariance structures. Results show that QDA is competitive under most settings, but can be outperformed by other classifiers with increasing sample size and when the covariance structures across classes are similar. Other noteworthy results include sensitivity of DQDA to non-normality and dependence of the performance of GQDA on whether sample sizes are balanced or not.