Comparing two statistical distribution methods is one of the most important topics which have been studied over the last four decades. The simplest method used in this field is to compare the mean of the underlying distributions and in the case of equal means, to compare theirs variances. In order to make more accurate and more comperhensive comparisons, it is better to compare the probability distributions. In this context researchers introduced a new and useful approach called stochastic orderings. Stochastic orders between probability distributions is a widely studied concept. There are several kinds of stochastic orders that are used to compare different aspects of probability distributions like location, variability, skewness, dependence, etc. It is used in many branches of statistics and probability such as reliability, queuing theory and survival analysis. order statistics play a vital role in the lifetime studies and statistical inferences of parameters. These order statistics are equal to the lifetime of k-out-n systems, in the field of reliability. Therefore the stochastic comparisons of order statistics have been considered by many researchers. In the literature, the random variables are considered independent and identically distributed, while it does not occur in practice. In this thesis the comparisons of order statistics using the most common stochastic orders for different conditions of samples of random variables including independent and non-identical, dependent and identical and dependent and non-identical are investigated.