In case you are interested in a mathematical treatment (maybe the followig is not what you are looking for, but I guess my answer doesn't hurt):

• In modern treatments of classical mechanics, time is modeled as a 1-dim. euclidean space $E^1$. The two orientations of the translation space correspond to future- and past-pointing vectors. In addition, absolute time is postulated - a map $M\to E^1$ defined on the spacetime manifold $M$.
• As you certainly know, absolute time is not existent in special relativity: Two events that are simultaneous for a given observer will not necessarely be so for a second observer. If you are interested in more details and a very modern mathematical approach to special relativity (postulating that spacetime is a 4-dim. affine space (not $\mathbb{R}^4$) with a bilinear form on the translation space), then I suggest you have a look at Éric Gourgoulhon's Special Relativity in General Frames. It has nice sections on proper time (chapter 2) and observers (chapter 3).