  The purpose of the present work is to provide short and supple teaching notes
for a $30$ hours introductory course on elementary \textit{Enumerative
Algebraic Combinatorics}. We fully adopt the \textit{Rota way} (see, e.g.
\cite{KY}). The themes are organized into a suitable sequence that allows us to
derive any result from the preceding ones by elementary processes. Definitions
of \textit{combinatorial coefficients} are just by their \textit{combinatorial
meaning}. The derivation techniques of formulae/results are founded upon
constructions and two general and elementary principles/methods:
  - The \textit{bad element} method (for \textit{recursive} formulae). As the
reader should recognize, the bad element method might be regarded as a
combinatorial companion of the idea of \textit{conditional probability}.
  - The \textit{overcounting} principle (for \textit{close form} formulae).
  Therefore, \textit{no computation} is required in \textit{proofs}:
\textit{computation formulae are byproducts of combinatorial constructions}. We
tried to provide a self-contained presentation: the only prerequisite is
standard high school mathematics. We limited ourselves to the
\textit{combinatorial point of view}: we invite the reader to draw the
(obvious) \textit{probabilistic interpretations}.
