| 1 | The Idea of a Riemann Surface | PDF unavailable |
| 2 | Simple Examples of Riemann Surfaces | PDF unavailable |
| 3 | Maximal Atlases and Holomorphic Maps of Riemann Surfaces | PDF unavailable |
| 4 | A Riemann Surface Structure on a Cylinder | PDF unavailable |
| 5 | A Riemann Surface Structure on a Torus | PDF unavailable |
| 6 | Riemann Surface Structures on Cylinders and Tori via Covering Spaces | PDF unavailable |
| 7 | Moebius Transformations Make up Fundamental Groups of Riemann Surfaces | PDF unavailable |
| 8 | Homotopy and the First Fundamental Group | PDF unavailable |
| 9 | A First Classification of Riemann Surfaces | PDF unavailable |
| 10 | The Importance of the Path-lifting Property | PDF unavailable |
| 11 | Fundamental groups as Fibres of the Universal covering Space | PDF unavailable |
| 12 | The Monodromy Action | PDF unavailable |
| 13 | The Universal covering as a Hausdorff Topological Space | PDF unavailable |
| 14 | The Construction of the Universal Covering Map | PDF unavailable |
| 15 | Completion of the Construction of the Universal Covering: Universality of the Universal Covering | PDF unavailable |
| 16 | Completion of the Construction of the Universal Covering: The Fundamental Group of the base as the Deck Transformation Group | PDF unavailable |
| 17 | The Riemann Surface Structure on the Topological Covering of a Riemann Surface | PDF unavailable |
| 18 | Riemann Surfaces with Universal Covering the Plane or the Sphere | PDF unavailable |
| 19 | Classifying Complex Cylinders: Riemann Surfaces with Universal Covering the Complex Plane | PDF unavailable |
| 20 | Characterizing Moebius Transformations with a Single Fixed Point | PDF unavailable |
| 21 | Characterizing Moebius Transformations with Two Fixed Points | PDF unavailable |
| 22 | Torsion-freeness of the Fundamental Group of a Riemann Surface | PDF unavailable |
| 23 | Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian Fundamental Groups | PDF unavailable |
| 24 | Classifying Annuli up to Holomorphic Isomorphism | PDF unavailable |
| 25 | Orbits of the Integral Unimodular Group in the Upper Half-Plane | PDF unavailable |
| 26 | Galois Coverings are precisely Quotients by Properly Discontinuous Free Actions | PDF unavailable |
| 27 | Local Actions at the Region of Discontinuity of a Kleinian Subgroup of Moebius Transformations | PDF unavailable |
| 28 | Quotients by Kleinian Subgroups give rise to Riemann Surfaces | PDF unavailable |
| 29 | The Unimodular Group is Kleinian | PDF unavailable |
| 30 | The Necessity of Elliptic Functions for the Classification of Complex Tori | PDF unavailable |
| 31 | The Uniqueness Property of the Weierstrass Phe-function associated to a Lattice in the Plane | PDF unavailable |
| 32 | The First Order Degree Two Cubic Ordinary Differential Equation satisfied by the Weierstrass Phe-function | PDF unavailable |
| 33 | The Values of the Weierstrass Phe-function at the Zeros of its Derivative are nonvanishing Analytic Functions on the Upper Half-Plane | PDF unavailable |
| 34 | The Construction of a Modular Form of Weight Two on the Upper Half-Plane | PDF unavailable |
| 35 | The Fundamental Functional Equations satisfied by the Modular Form of Weight Two on the Upper Half-Plane | PDF unavailable |
| 36 | The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the Upper Half-plane | PDF unavailable |
| 37 | The Weight Two Modular Form Vanishes at Infinity | PDF unavailable |
| 38 | The Weight Two Modular Form Decays Exponentially in a Neighbourhood of Infinity | PDF unavailable |
| 39 | A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism onto the Upper Half-Plane | PDF unavailable |
| 40 | The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic Curve | PDF unavailable |
| 41 | A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-Invariant | PDF unavailable |
| 42 | The Fundamental Region in the Upper Half-Plane for the Unimodular Group | PDF unavailable |
| 43 | A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly Once | PDF unavailable |
| 44 | Moduli of Elliptic Curves | PDF unavailable |
| 45 | Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-Space | PDF unavailable |
| 46 | The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane Curve | PDF unavailable |
| 47 | Complex Projective 2-Space as a Compact Complex Manifold of Dimension Two | PDF unavailable |
| 48 | Complex Tori are the same as Elliptic Algebraic Projective Curves | PDF unavailable |