The aim of this thesis is to propose, implement, and evaluate an automatic method for the segmentation of cell nucleus instances in large three-dimensional fluorescence microscopy image data. The proposed segmentation method uses a fully convolutional neural network to predict a binary mask of cell nuclei. Individual cell nucleus instances are then segmented using the Watershed algorithm. The thesis contains a description of the individual steps of the segmentation method, a justification for the chosen approach, as well as a quantitative evaluation of the results. An implementation of the developed method in the Python programming language is a part of the thesis.