Unequal Probability Sampling has been efficiently used for estimation of population characteristics. Several developments have been made from time to time to increase the precision of estimates. In this book we present some new methods of estimation in unequal probability sampling. Some selection procedures have been discussed for use with the Horvitz and Thompson (1952) estimator. We have also proposed a general selection procedure which yields several selection procedures as special case. We have also discussed the method of developing the approximations for variance formulae for Horvitz and Thompson (1952) estimator. Some new estimators have been discussed alongside their design and model based study. The empirical comparison of proposed techniques has also been given with some well known estimation techniques of unequal probability sampling.