The Main Author Of This Work Is Experienced Author And Researcher. He Found That A Book Conveying The Needed Sophisticated Tools Is Missing In The Growing Community. Most Books On Planetary Systems And Exoplanets Do Not Cover The Critical Problems Of Dynamics And Stability In Sufficient Depth. In Order To Calculate Potential Scenarios In Distant Systems, Researchers Need A Book That Conveys The Needed Mathematical Methods In An Accessible Way. This Book Does That By Using The Software Mathematica. 1. Introduction Dawn Of Astronomy: Observations From Babylon Three Major Steps: Computer - Chaos - Extrasolar Planets Outlook Interplanetary Space Flights 2. Basics The Pendulum As Dynamical Model Perturbed Pendulum Standard Map Chaos Indicators Correspondance Mappings - Dynamical Systems Resonances 3. Numerical And Analytical Tools Lie - Operator And Lie - Series Lie - Series As Num. Integrators Lie - Transformation And Hamiltonian Normal Forms Other Applications Of Lie - Series 4. Intermezzo 1: The Sitnikov Problem 5. The 2 - Body Problem Orbital Elements Kepler´S Laws Kepler´S Equation Applications 6. The 3 - Body Problem Newtonian Vs. Hamiltonian Formulation Correspondance: Resonant Motion And The Perturbed Pendulum Disturbing Function Mapping Models 7. Intermezzo 2: Effective Stability - The Nekhoroshev Theorem 8. The Planetary Problem 9. Dynamics Of Exo - Planetary Systems 10. Appendix: Interactive Demonstrations Based On Mathematica