Ranking issues are found everywhere. For example, bank houses, universities, towns, watersheds etc. are ranked. But also assessment of students in one discipline is a ranking. This last example is trivial, because we have only one criterion, namely the quality of the student in that discipline. In the other cases ranking can be a very hard job. Why? There is often no measure. How do we measure towns with respect to living quality? How do we measure the hazard exerted by chemicals? No chemical has its intrinsic identity card where its hazard can be identified. Thus multi-indicator systems come into play. We gather indicators which help to characterize the items of interest for ranking. Measurement of indicators, selecting indicators, testing indicators. And we arrive at a multi-indicator system. We have gathered useful information for ranking. However, we do not know how to derive ranking from the multitude of valuable information. In a popular approach, the indicator values are weight-averaged. The resulting weighted averages are used to obtain the ranking. We offer the mathematical tool of partial order as a tool to get insight into the process, starting with the multi-indicator system and finishing up with ranking. Application of partial order involving multi-indicator systems is in its initial phases and is advancing with more and more tools. This book provides a timely introduction to the partial order theory and its techniques with worked out illustrations and applications to a variety of live case studies. It is written for interested social and technical scientists, statisticians, , computer scientists, and graph theorists, stakeholders, instructors, and students at graduate and senior undergraduate levels. We have enjoyed writing it. You will hopefully enjoy reading it and using it.