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Guided by the laws of thermodynamics, phase diagrams can be constructed to display First Order phase transformations (Gibbsian), as well as Higher Order phase transitions (non-Gibbsian). We discuss one and two-component alloy systems in this paper. The principles of the construction of phase diagrams are presented and some of the documented construction errors mentioned in the literature that can arise in phase diagram construction are noted and discussed. We go on to discuss what have been termed “probable errors” of construction. These are constructions which could only arise from the application of highly unlikely solution thermodynamic expressions. We then discuss the application of the Third Law of Thermodynamics to illustrate how phase boundary extrapolations to low temperatures can sometimes be shown to be in error. In addition, errors which may arise in the construction of phase diagrams that include higher order thermodynamic transitions (e.g. magnetic or atomic ordering) are briefly mentioned. These construction rules and comments should be of help to scientists who rely on phase diagrams in the development of materials. Also, we hope that it will be of help to those who utilize computer programs and compilations to display their modeled phase diagrams properly.