UNITARY REPRESENTATIO N THEORY FOR SOLVABLE LIE GROUPS CONTENTS P r e f a c e . Contents . I. Introduction. II. Algebrai c P r e l i m i n a r i e s . 1. Notation 2. Almos t Algebrai c Lie Algebras . 3. Ad-algebrai c hulls . III. The Co-adjoint Representation . 0. Introduction. 1. Two examples . 2. Two basi c operations . 3. When can operation II be applied? 4. Main r e s u l t s . 5. Example s and complements . 6. Ad v e r s u s ad IV. R e p r e s e n t a t i o n - T h e o r e t i c P r e l i m i n a r i e s . 1. Conventions. 2. On action. 3. The Kirillov correspondence . 4. Miscellany. 5. Notation. V. The Mackey Obstruction . 1. Introduction. 2. A specia l c a s e . 3. The genera l c a s e . 4. The little-grou p t h e o r e m .

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