1. INTRODUCTION -- 2. THE INVARIANTS -- 3. QUASI-ISOMORPHISM -- 4. CHANGE OF BASIS -- 5. DECOMPOSITIONS OF RANK TWO GROUPS -- 6. QUOTIENT DIVISIBLE GROUPS -- 7. THE TYPES OF ELEMENTS -- 8. ENDOMORPHISMS -- 9. ISOMORPHISMS OF QUASI-ISOMORPHIC GROUPS -- 10. CONJECTURES AND QUESTIONS CONCERNING GROUPS OF ARBITRARY FINITE RANK -- REFERENCES