A simulation that has any random aspects involves sampling, or generating random variates from probability distributions. There are situations in the practice of statistical research where continuous distributions are not characterized by their density or cumulative distribution function. Constructing such algorithms is a special problem of random variate generation. The objective of this work is to implement, test and improve these algorithms. It is investigated whether such algorithms in the literature can be used in practice, namely, in simulation. In the first part, the book provides a basic introduction to random variate generation. Then the testing methods for random variate generation algorithms used in this book are formulated. Afterwards, it is described how to generate random variates if only the Fourier coefficients of the desired distribution are known. It then deals with generating random variates from a distribution where just a few moments are known. The next part includes five different algorithms about generation of vectors where only correlation and marginal distribution are known. In the end, C codes of all algorithms in the book are given.