In the first months of 2001 the AGN Mkn 421 showed highly variable, strong TeV activity at flux levels frequently exceeding 1 Crab. Here we present the light curve and energy spectrum of Mkn 421 as measured with the HEGRA stand alone telescope CT1. Around 30% of the data were taken under moonlight conditions. The spectrum shows a significant exponential energy cutoff at around 3.4 TeV. The results from the dark night- and the moon data are in excellent agreement with each other. A significant spectral shape variation depending on the flux level has been found. The TeV light curve is also found to be highly correlated with the X-ray light curve of the RXTE/ASM satellite, showing no significant time lag larger than 0.2 d. The derived correlation coefficient of 0.83 corresponds to a 5.2 σ significance.