The concept of *Shannon's entropy* (Shannon's (1948) [86])
is the central role of information theory sometimes referred as *measure
of uncertainty*. The entropy of a random variable is defined in terms
of its probability distribution and can be shown to be a good measure of
randomness or uncertainty. This chapter mainly deals with its characterizations
and properties. Properties for discrete finite random variable are studied.
The study is extended to random vectors with finite and infinite values.
The idea of entropy series is explained. Finally, the continuous case generally
referred as
*differential entropy* with different probability distributions
and power inequality are studied.

21-06-2001 Inder Jeet Taneja Departamento de Matemática - UFSC 88.040-900 Florianópolis, SC - Brazil