Beam instabilities is a research field within accelerator physics and plasma physics that investigates collective phenomena in charged particle beams. It focuses on the mechanisms by which small perturbations within the beam or its surrounding environment grow exponentially, leading to degradation, emittance growth, or loss of the beam. Key characteristics involve the collective interaction between beam particles or between the beam and its environment (such as vacuum chamber walls or electromagnetic fields), manifesting in various modes (e.g., transverse, longitudinal, resistive wall, wakefield); their significance lies in the critical need to understand and mitigate these effects for the successful design, operation, and performance optimization of particle accelerators, fusion devices, and other beam-based technologies.