Linear discriminant analysis (LDA) is a versatile statistical method for reducing redundant and noisy information from an original sample to its essential features. Particularly, LDA is a supervised learning technique, in which the labelled data are necessary for its training process and have been widely used for data dimensionality reduction. Original data are transformed into a low-dimensional subspace by maximizing the trace of the between-class scatter matrix while minimizing the trace of the within-class scatter matrix, thereby enhancing the expressiveness of features. This Primer offers a thorough overview of LDA, including its definition and the interpretation of its numerical and graphical results. It details LDA variants, their implementation settings, experimental outcomes and widely used open-source databases. This Primer also explores applications of LDA-based methods, implementation details across various areas and connections with related methodologies. Reproducibility, limitation and optimization of LDA-based methods are discussed followed by future goals of LDA and its variants.