ONE OF THE MOST IMPORTANT SCIENTIFIC DEVELOPMENTS IN RECENT YEARS IS THE DISCOVERY OF LARGE NUMBERS OF EXOPLANETARY SYSTEMS. PARTICULARLY NOTEWORTHY IS THE SUCCESS OF NASA S KEPLER MISSION WHICH HAS DISCOVERED 3606 PLANETARY SYSTEM CANDIDATES CONTAINING NEARLY 4 700 PLANET CANDIDATES USING THE TRANSITING METHOD OF WHICH 733 ARE MULTI-PLANET SYSTEMS. THE DISCOVERED EXO-PLANETARY SYSTEMS BEAR LITTLE RESEMBLANCE TO OUR OWN SOLAR SYSTEM: MOST OF THE KEPLER PLANETS ARE SUPER-EARTHS OR MINI-NEPTUNES AND HAVE ORBITAL PERIODS SHORTER THAN 200 DAYS. SOME OF THESE SYSTEMS ARE VERY TIGHTLY PACKED FEATURING VERY LOW ORBITAL ECCENTRITIES AND INCLINATIONS. THE DISCOVERY OF SUCH EXOPLANETARY SYSTEMS CHALLENGES EXISTING UNDERSTANDINGS OF PLANETARY SYSTEMS WHILE EXPOSING FERTILE NEW AREAS OF RESEARCH IN PLANETARY DYNAMICS. IN LIGHT OF THESE CURRENT CHALLENGES I PROPOSE TO CONDUCT RESEARCHES TO STUDY THE DYNAMICAL EVOLUTION OF SUCH MULTI-PLANET SYSTEMS WITH PARTICULAR EFFORTS TOWARDS UNDERSTANDING THE ARCHITECTURES FORMATION AND EVOLUTION OF SUCH SYSTEMS. MY PROPOSED RESEARCH CONSISTS OF THREE INTER-RELATED PROJECTS. PROJECT I - DYNAMICAL EVOLUTION OF MULTI-PLANET SYSTEMS WITH EXTERNAL COMPANIONS: RECENT OBSERVATIONS HAVE REVEALED THE EXISTENCE OF STELLAR BINARY COMPANIONS OR EXTERNAL GIANT PLANET COMPANIONS AROUND A NUMBER OF MULTI-PLAET SYSTEMS. WHAT IS THE EVOLUTION OF SUCH SYSTEMS WITH OUTER COMPANIONS? WHAT HAPPENS IF THERE IS AN UNSTABLE SYSTEM OF GIANT PLANET COMPANIONS? TO ANSWER THESE QUESTIONS I WILL EMPLOY A COMBINATION OF SEMI-ANALYTIC SECULAR PERTURBATION THEORY AS WELL AS N-BODY SIMULATIONS. PROJECT II - FATE OF UNSTABLE MULTI-PLANET SYSTEMS: NUMERICAL EXPERIMENTS SUGGEST THAT MANY DISCOVERED MULTI-PLANET SYSTEMS ARE AT THE EDGE OF STABILITY: IF THE PLANETS WERE PLACED ANY CLOSER THEY WOULD UNDERGO COLLISIONS OR EJECTIONS WITHIN THE LIFETIME OF THE SYSTEM. DOES THIS PROCESS OCCUR INDEFINITELY RESULTING IN THE ULTIMATE DESTRUCTION OF ALL OR MOST PLANETS OR DOES THE SYSTEM EVENTUALLY FIND A NEW STABLE CONFIGURATION? I PLAN TO RESEARCH THIS TOPIC USING N-BODY SIMULATIONS COMBINED WITH A SEMI-ANALYTIC PRESCRIPTION FOR THE OUTCOMES OF PLANETARY COLLISIONS. PROJECT III - INTERFACING THEORETICAL RESULTS WITH OBSERVATIONAL DATA: A NATURAL EXTENSION TO PROJECTS I AND II IS TO COMBINE THEIR THEORETICAL UNDERSTANDINGS WITH OBSERVATIONAL DATA TO MAKE INFERENCES ABOUT THE STATISTICAL PROPERTIES OF PLANETARY SYSTEMS. I WILL APPLY ATTAINED RESULTS IN COMBINATION WITH STATISTICAL TECHNIQUES TO MAKE CONSTRAINTS ON THE PREVALENCE OF OUTER COMPANIONS TO MULTI-PLANET SYSTEMS AND INFER THE PRIMORDIAL CONFIGURATIONS OF NEWLY BIRTHED PLANETARY SYSTEMS. THROUGH ANSWERING THESE QUESTIONS MY WORK WILL ADVANCE NASA'S GOALS TOWARDS UNDERSTANDING THE ARCHITECTURES FORMATION AND EVOLUTION OF PLANETARY SYSTEMS. IN CONCERT WITH NASA'S OBJECTIVES MY PROPOSED WORK PROVIDES FUNDAMENTAL RESEARCH AND ANALYSIS NECESSARY TO CHARACTERIZE OTHER PLANETARY SYSTEMS AND RELATES TO THE UNDERSTANDING OF DYNAMICS AND ENERGETICS OF EXOPLANETARY SYSTEMS.