As we all know that sampling with unequal probability plays most
important role in large scale sample surveys, therefore in this
monograph some recent developments regarding this topic has been
discussed. Moreover since joint probability is difficult calculate
therefore some approximations of the joint probability have been
derived. Special attention has been given to general theory of arbitrary
probability. For this theory sampling with replacement and without
replacement are the special cases of this general theory. Generalized
Murthy estimator has also been discussed in details.