In the preceding chapters it has generally been stated that either simple random samples (SRS) have been obtained or that samples are considered as though they had been obtained using an SRS procedure. In this chapter SRS are analyzed in the context of a population of known size. The finite population correction is deduced from both randomization theory and a model based approach. A case study involving the loading of rocks onto barges is presented. Stratified sampling is then introduced and the optimal allocation of a sample over strata is obtained. Multi-stage sampling is introduced. Quota sampling is discussed. Results for ratio and regression estimators are derived. A final case study is that of an asset management plan for a large water company which shows that efficiency of techniques such as stratification and ratio estimation. The case study demonstrates the importance distinguishing between sampling errors that reduce if larger samples are taken from the system, in order to assess the work to be done, and calibration errors in a unit cost data base that will persist however much sampling of work to be done is carried out. The chapter ends with: a summary of: notation used; the main results, MATLAB and R syntax; and exercises.