How do objects orbit if more than 2 massive bodies are involved? Newton's versions of Keplers 3 Laws of Planetary Motion are only strictly valid for 2 massive bodies. The Solar System, however, clearly has more than 2 massive objects within it. How do we handle this many-body problem? This lecture discusses some of the multi-body gravitational effects seen in our Solar System (and by extension elsewhere). We will describe Lagrange Points for the restricted 3-body problem and consequences like the Trojan Asteroids of Jupiter, long-range gravitational perturbations and their aid in discovering the planet Neptune, close encounters that can dramatically alter the orbits of comets and give us ways to slingshot spacecraft into the outer and inner Solar System without huge expenditures of fuel, and orbital resonances that can amplify small long-range perturbations and either stabilize or destabilize orbits. All of these effects play a role in the Dynamical Evolution of our Solar System that we will see throughout later parts of the course. Recorded 2007 Oct 18 in 1000 McPherson Lab on the Columbus campus of The Ohio State University.