In this work we review the development of the generalized theory of capillarity. When considering the theory of contact lines, we find that the theory developed by Boruvka and Neumann (BN) requires significant modifications. Their choice of parameters (independent variables) for a line is insufficient for formulating the fundamental equation. Furthermore, there are differential geometric constraints on these geometric parameters but not included in their analysis. As a result, their independent variables are in fact dependent. To describe the geometry of contact lines properly, we present a new set of parameters from the differential geometry viewpoint and subsequently give the fundamental equation for the thermodynamic system of contact lines. (C) 2003 Elsevier Science (USA). All rights reserved.