1. The subject of investigation
2. The fundamental functions on a Riemann surface
3. The infinities of rational functions
4. Specification of a general form of Riemann's integrals
5. Certain forms of the fundamental equation of the Riemann surface
6. Geometrical investigations
7. Coordination of simple elements
8. Abel's theorem
9. Jacobi's inversion problem
10. Riemann's theta functions
11. The hyperelliptic case of Riemann's theta functions
12. A particular form of Riemann surface
13. Radical functions
14. Factorial functions
15. Relations concerning products of theta functions
16. A direct method of obtaining the equations relating theta functions
17. Theta relations with certain groups of characteristics
18. Transformation of periods
19. On systems of periods and on general Jacobian functions
20. Transformation of theta functions
21. Complex multiplication of theta functions
22. Degenerate Abelian integrals
Appendix 1. On algebraic curves in space
Appendix 2. On matrices.
