TABLE OF CONTENTS -- ABSTRACT -- INTRODUCTION -- CHAPTER I: PRELIMINARIES AND HONG'S THEOREM -- CHAPTER II: SOME MODULAR LATTICES WITH FOUR GENERATORS -- CHAPTER III: THE FUNDAMENTAL THEOREM ON WEAK ATOMICITY -- CHAPTER IV: THE MAIN STRUCTURE THEOREM -- CHAPTER V: APPLICATIONS -- APPENDICES A: M[sup()][sub(5)] IS NOT FINITELY BASED -- APPENDICES B: A GENERAL EMBEDDING THEOREM -- REFERENCES