We have analyzed Goddard High Resolution Spectrograph data of eight classical T Tauri stars (CTTSs) and one weak-lined T Tauri star (WTTS). The GHRS data consist of spectral ranges 40 Å wide centered on 1345, 1400, 1497, 1550, and 1900 Å. These UV spectra show strong Si IV and C IV emission and large quantities of sharp (~40 km s^-1) H₂ lines. All the H₂ lines belong to the Lyman band, and all the observed lines are single peaked and optically thin. The averages of all the H₂ lines centroids for each star are negative, which may indicate that they come from an outflow. We interpret the emission in H₂ as being the result of fluorescence, mostly by H_Lyα, and identify seven excitation routes within 4 Å of that line. We obtain column densities (10¹²-10¹⁵ cm^-2) and optical depths (~1 or less) for each exciting transition. We conclude that the populations are far from being in thermal equilibrium. We do not observe any lines excited from the far blue wing of H_Lyα, which implies that the molecular features are excited by an absorbed profile. Si IV and C IV (corrected for H₂ emission) have widths of ~200 km s^-1 and an array of centroids (blueshifted lines, centered, redshifted). These characteristics are difficult to understand in the context of current models of the accretion shock. For DR Tau we observe transient strong blueshifted emission, perhaps the result of reconnection events in the magnetosphere. We also see evidence of multiple emission regions for the hot lines. While C IV is optically thin in most stars in our sample, Si IV is not. However, C IV is a good predictor of Si IV and H₂ emission. We conclude that most of the flux in the hot lines may be caused by accretion processes, but the line profiles can have multiple and variable components.

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