  This manuscript includes some classical results we select apart from the new
results we've found on the Analysis of Boolean Functions and
Fourier-Entropy-Influence conjecture. We try to ensure the self-completeness of
this work so that readers could probably read it independently. Among the new
results, what is the most remarkable is that we prove that the entropy of a
boolean function $f$ could be upper bounded by
$O(I(f))+O(\sum\limits_{k}I_k(f)\log (1/I_k(f)))$.
