The present dissertation was developed with the main objective of studying and classifying the generic singularities existing on surfaces with Gaussian curvature K = −1 in R(3). More specifically, we begin our study by defining the asymptotic parameterizations and the Tchebyshev network, obtaining the so-called sine-Gordon equation. Next, we present characteristics about the generating function and make a correlation between it and the singularities of the associated surface. Finally, we state and demonstrate a theorem that allows the location and classification of singularities of a generic pseudospherical surface.