In this thesis, we will present some methods for data discrimination and classification. At the beginning, we will define criteria for optimal data classification, and later on, we will explain the methods for evaluating classification functions and how to calculate the error rates in classification. In the second chapter, we will list several methods for classification with two multivariate normal populations in the case when covariance matrices are equal and in the case when they are not. In the fourth chapter, we will deal with classification with several populations. We will also mention Fisher’s approach to classification. In the fifth chapter, we will describe logistic regression as another method for data classification and discrimination. In the sixth chapter, we will solve and explain several examples on various data to better understand the application of the mentioned classification rules in practice. We will see that there is no unique answer to which method is best for classification, and we will base our conclusions on the assumptions of classification rules and error rates.