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TESS photometry is analyzed for 432 classical Be stars observed in the first year of the mission. The often complex and diverse variability of each object in this sample is classified to obtain an understanding of the behavior of this class as a population. 98\% of the systems are variable above the noise level, with timescales spanning nearly the entire range of what is accessible with TESS, from tens of minutes to tens of days. The variability seen with TESS is summarized as follows. Nearly every system contains multiple periodic signals in the frequency regime between about 0.5 -- 4 d$^{-1}$. One or more groups of closely-spaced frequencies is the most common feature, present in 85\% of the sample. Among the Be stars with brightening events that are characteristic of mass ejection episodes (17\% of the full sample, or 30\% of early-type stars), all have at least one frequency group, and the majority of these (83\%) show a concurrent temporary amplitude enhancement in one or more frequency groups. About one third of the sample is dominated by low frequency ($f < 0.5$ d$^{-1}$, and often much lower) variability. Stochastic signals are prominent in about 26\% of the sample, with varying degrees of intensity. Higher frequency signals ($6 < f < 15$ d$^{-1}$) are sometimes seen (in 14\% of the sample) and in most cases likely reflect p mode pulsation. In rare cases ($\sim$3\%), even higher frequencies beyond the traditional p mode regime ($f > 15$ d$^{-1}$) are observed.