This tutorial review by Murray, Brunet, and Michel details the rationale and implementation of a set of analyses for surface-recorded event-related potentials (ERPs) that utilize high-density electrode montages to provide reference-free spatial information. These analyses help in understanding modulations in response strength, latency, and topography between and within experimental conditions, offering more neurophysiologically interpretable information compared to canonical waveform analyses. The tutorial uses somatosensory evoked potentials (SEPs) in response to hand stimulation as an example to illustrate these methods. It covers the conceptual and mathematical aspects of each step, including the interpretation of statistical outcomes. The review emphasizes the importance of topographic analysis in removing experimenter bias and identifying information within high-density ERP datasets. Key methods discussed include Global Field Power (GFP) for measuring response strength, Global Dissimilarity (DISS) for quantifying response topography, and topographic pattern analysis for identifying stable periods of topographic stability. The tutorial also addresses the limitations of canonical waveform analyses, such as reference-dependent results, and provides practical guidance on data normalization and artifact handling.This tutorial review by Murray, Brunet, and Michel details the rationale and implementation of a set of analyses for surface-recorded event-related potentials (ERPs) that utilize high-density electrode montages to provide reference-free spatial information. These analyses help in understanding modulations in response strength, latency, and topography between and within experimental conditions, offering more neurophysiologically interpretable information compared to canonical waveform analyses. The tutorial uses somatosensory evoked potentials (SEPs) in response to hand stimulation as an example to illustrate these methods. It covers the conceptual and mathematical aspects of each step, including the interpretation of statistical outcomes. The review emphasizes the importance of topographic analysis in removing experimenter bias and identifying information within high-density ERP datasets. Key methods discussed include Global Field Power (GFP) for measuring response strength, Global Dissimilarity (DISS) for quantifying response topography, and topographic pattern analysis for identifying stable periods of topographic stability. The tutorial also addresses the limitations of canonical waveform analyses, such as reference-dependent results, and provides practical guidance on data normalization and artifact handling.