The contemporary understanding of matter is based on the quantum theory, which envisions large collections of particles interacting with each other and with their environment. Spectroscopic probes based for instance on light change the environment and trigger a collective response of the particles. This book based on a graduate-level course explains the underpinnings of many-body quantum theory and exposes the main methodologies for calculations, before describing, with the support of practical examples and short computer codes, how the spectroscopic techniques are represented within the theory and how their outcome is interpreted as a probe of the correlations between quantum particles.