The Lindhard response function is a theoretical framework used to describe the dynamical polarization of a many-body electron system in response to an external perturbation, such as an electric field or a photon. It provides a formalism for calculating the dielectric function and related properties of materials, considering the collective behavior of electrons. Dynamical charge and spin waves are collective excitations of the charge and spin degrees of freedom in a material, respectively. These waves arise due to the interaction between electrons and their environment, Fig. Constant-current STM image of Cu(111) surface. Friedel oscillations from point defects and step edges are clearly visible. Friedel oscillations can be identified by their long-range wave-like pattern. Reprinted with permission from Crommie et. al. leading to coherent motion of charge or spin carriers. Dynamical charge and spin waves are described within the framework of many-body theory and play essential roles in phenomena such as magnetism and transport. These four concepts are interconnected through their description of the collective behavior of electrons in condensed matter systems and their response to external perturbations. Dynamical polarization and the Lindhard response function provide theoretical frameworks for understanding the electronic response to external fields, while Friedel oscillations and dynamical charge/spin waves are manifestations of the collective behavior of electrons in materials, influenced by interactions with impurities, defects, and other environmental factors.