This article provides a tutorial on the practical application of PARAFAC (Parallel Factor Analysis) to fluorescence excitation emission matrices (EEMs). PARAFAC is used to decompose EEMs into their underlying chemical components, enabling the identification and quantification of independently varying fluorophores. The tutorial demonstrates this using a dataset of dissolved organic matter (DOM) fluorescence. A new MATLAB toolbox is introduced to support improved visualization and sensitivity analysis of PARAFAC models in fluorescence spectroscopy. PARAFAC is a multi-way method applicable to data arranged in three- or higher-order arrays. It decomposes three-way datasets into trilinear terms and a residual array. The method is particularly useful for fluorescence EEMs, where it can identify and quantify chemical components. However, challenges such as correlated components, systematic errors, and non-linearities due to the inner filter effect can complicate the analysis. The tutorial outlines the steps involved in PARAFAC analysis, including data import, preprocessing, exploratory data analysis, model validation, and interpretation. Preprocessing steps include data correction, elimination of non-trilinear data, and normalization of signals. Model validation involves assessing the number of components and ensuring the model adheres to the variability assumption. Split-half analysis is used to confirm the robustness of the model. The article also discusses the interpretation of PARAFAC results, emphasizing the importance of chemical interpretation and the challenges in interpreting organic matter fluorescence. It highlights the need for careful model validation and the use of appropriate constraints to ensure stable and chemically meaningful solutions. The tutorial dataset and toolboxes are provided for further analysis.This article provides a tutorial on the practical application of PARAFAC (Parallel Factor Analysis) to fluorescence excitation emission matrices (EEMs). PARAFAC is used to decompose EEMs into their underlying chemical components, enabling the identification and quantification of independently varying fluorophores. The tutorial demonstrates this using a dataset of dissolved organic matter (DOM) fluorescence. A new MATLAB toolbox is introduced to support improved visualization and sensitivity analysis of PARAFAC models in fluorescence spectroscopy. PARAFAC is a multi-way method applicable to data arranged in three- or higher-order arrays. It decomposes three-way datasets into trilinear terms and a residual array. The method is particularly useful for fluorescence EEMs, where it can identify and quantify chemical components. However, challenges such as correlated components, systematic errors, and non-linearities due to the inner filter effect can complicate the analysis. The tutorial outlines the steps involved in PARAFAC analysis, including data import, preprocessing, exploratory data analysis, model validation, and interpretation. Preprocessing steps include data correction, elimination of non-trilinear data, and normalization of signals. Model validation involves assessing the number of components and ensuring the model adheres to the variability assumption. Split-half analysis is used to confirm the robustness of the model. The article also discusses the interpretation of PARAFAC results, emphasizing the importance of chemical interpretation and the challenges in interpreting organic matter fluorescence. It highlights the need for careful model validation and the use of appropriate constraints to ensure stable and chemically meaningful solutions. The tutorial dataset and toolboxes are provided for further analysis.