The impossibility to reach an entire population, owing to time and budget constraints, results in the need for sampling to estimate population parameters. There are various methods of sampling and this thesis deals with a specific method of probability sampling, known as systematic sampling. Problems within the systematic sampling context include: (i) If the size of the population is not a multiple of the size of the sample, then conventional systematic sampling (also known as linear systematic sampling) will either result in variable sample sizes, or constant sample sizes that are greater than required; (ii) Linear systematic sampling is not the most preferred probability sampling design for populations that exhibit linear trend; (iii) An unbiased estimate of the sampling variance cannot be obtained from a single systematic sample. I will attempt to make an original contribution to the current body of knowledge, by introducing three new modified systematic sampling designs to address the problems mentioned in (ii) and (iii) above. We will first discuss the measures to compare the various probability sampling designs, before providing a review of systematic sampling. Thereafter, the methodology of linear systematic sampling will be examined as well as two other methodologies to overcome the problem in (i). We will then obtain e fficiency related formulas for the methodologies, after which we will demonstrate that the e fficiency of systematic sampling depends on the correlation of the population units, which in turn depends on the arrangement and structure of the population. As a result, we will compare linear systematic sampling with other common probability sampling designs, under various population structures. Further designs of linear systematic sampling (including a new proposed design), which are considered to be optimal for populations that exhibit linear trend, will then be examined to resolve the problem mentioned in (ii). Thereafter, we will tackle the problem in (iii) by exploring various strategies, which include two new designs. Finally, we will obtain numerical comparisons for all the designs discussed in this thesis, on various population structures, before providing a comprehensive report on the thesis.