The purpose of these lectures is to describe some of the dynamical phenomena that are important in the evolution of galaxies and clusters of galaxies. Galactic Dynamics is usually perceived as an arid discipline, whose mathematical formalism make it hard to apply to real astronomical problems. This is very unfortunate, since gravity is behind all astronomical phenomena and its resulting dynamics has a role to play. This misconception of Galactic Dynamics stems from the fact that often students are introduced to the subject using a formal approach, full of mathematical rigor, that leads through a lengthy path, before reaching astronomical applications. Although mathematical correctness is gained, a physical grasp of the dynamics behind is sometimes lost. It is our intention to bypass the usual formal introduction and to use an eclectic list of topics related to the dynamics of galaxies and clusters of galaxies, to illustrate the use of Galactic Dynamics. Our main goal is understanding, rather than rigor. We will attempt to show the student how, using some basic equations, we can extract useful dynamical information that can help in our understanding of the realm of galaxies. In Sect. 2, Poisson’s and Boltzmann’s equations are presented as the basic equations of Galactic Dynamics. After briefly reviewing what makes a dynamical system collisionless, we introduce in Sect. 3 one of the Jeans equations in spherical coordinates as a quick tool to derive the dynamical properties of a model built from a density profile, without having to build a self-consistent dynamical model. The Navarro, Frenk and White profile is used as an example. A Mathematica Notebook version of this section is provided as well. Students with access to this program can interact with this version and change parameters in the examples provided. The full Notebook is available from the Guillermo Haro and the author’s web pages. In Sect. 4 we mention two additional density profiles that can be used as exercises for the reader. We also note that simulations of interacting galaxies