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Series of outcomes, of conditions, of events regularly occur in our lives or they are encountered in our workplace, and sometimes they ought to be scrutinized. For example, we find at the factory that machine \#2 produces every day from 3 to 5 defective artifacts out of 20, or that early in the morning at the hospital emergency clinic, out of 112 patients examined, 28 had severe symptoms of enteritis. The systematic mathematical study of series was, as we know, first addressed to games of chance, at the same time as was probability theory. For example, throwing a coin $N$ times, what are the chances that we observe $n$ Face, or that the series of $N$ has $r$ runs (or sequences with results of the same side), or that the longest run has $L$ Face? Here we present a summary of the main results of the study of statistical series of $N$ items falling into 2 or $k$ (>2) categories, whether these items are provided from the outset or whether they emanate from a parameterized random process (binomial or multinomial). Formulas, examples and tables of critical values are provided.

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