Algebraic systems endowed with a partial or full order are; met with in several disciplines of mathematics. Because the; theory of partially ordered algebraic systems is extensive;' I have had to abandon the claim to completeness and to be — content with developing the main algebraic aspects of the theory. This is the reason why some important topics, such &s partially ordered linear or topological spaces, have not Ьеец. taken into consideration. Moreover, a certain limitation was* also necessary in the presentation of results which are purely: algebraic in character. To enable the reader to find out more, about the subject, references have been provided not only tp= the original sources of the material here collected, but also toz a number of important results which I have not been able to include. No attempt has been made to cover the whole vast: field of partially ordered algebraic systems in the bibliography,; but for the narrower field surveyed here, the bibliography, should be fairly complete. *i