This paper investigates the problem of finite-horizon H-infinity tracking for linear time-varying systems, Three tracking problems are considered, depending on whether the reference signal is perfectly known in advance, measured on-line, or previewed in fixed interval of time ahead. No a priori knowledge of a dynamic model for the reference signal is assumed. A game theory approach to the latter tracking problems is presented where, given a specific reference signal, the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise. Necessary and sufficient conditions for the existence of a saddle-point equilibrium are determined, and H-infinity tracking controllers for both the cases of state and output feedback are derived. Tracking problems far time-invariant systems on infinite-horizon are also analyzed, and time invariant tracking controllers are obtained for zero initial conditions.