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Density functional methods form the basis of a diversified and very active area of present days computational atomic, molecular, solid state and even nuclear physics. A large number of computational physicists use these meth­ ods merely as a recipe, not reflecting too much upon their logical basis. One also observes, despite of their tremendeous success, a certain reservation in their acceptance on the part of the more theoretically oriented researchers in the above mentioned fields. On the other hand, in the seventies (Thomas­ Fermi theory) and in the eighties (Hohenberg-Kohn theory), density func­ tional concepts became subjects of mathematical physics. In 1994 a number of activities took place to celebrate the thirtieth an­ niversary of Hohenberg-Kohn-Sham theory. I took this an occassion to give lectures on density functional theory to senior students and postgraduates in the winter term of 1994, particularly focusing on the logical basis of the the­ ory. Preparing these lectures, the impression grew that, although there is a wealth of monographs and reviews in the literature devoted to density func­ tional theory, the focus is nearly always placed upon extending the practical applications of the theory and on the development of improved approxima­ tions. The logical foundadion of the theory is found somewhat scattered in the existing literature, and is not always satisfactorily presented. This situation led to the idea to prepare a printed version of the lecture notes, which resulted in the present text.

Thermodynamics is considered to be an offshoot of the Industrial Revo­ lution that began in England in the second half of the 18th Century and from there spread to other parts of the world. The word thermodynamics is derived from the Greek therme (meaning heat) and dynamis (meaning force). As well known, the origins of thermodynamics are founded in the early 19th century in the study of the motive power of heat; that is, the capability of hot bodies to produce mechanical work. However, there are of course precursors to these ideas: Temperature is probably the earliest thermodynamic concept to attain operational status (early in the 17th century with Galileo). The science of calorimetry beginning in the late 18th century (contemporary with the beginning of the Indus­ trial Revolution) led to the establishment of the caloric theory of heat [5]. Clausius in the second half of the 19th century established Thermody­ namics as a clearly defined science. The connection of Thermodynamics with Mechanics is first achieved through kinetic theory with the work of D. Bernouilli, J Herapath, ]. ]. Waterston, R. Clausius, ]. c. Maxwell, and finally L. Boltzmann, later through Statistical Mechanics, whose main purpose is to determine the thermodynamic properties and values of macroscopic observables in terms of the dynamical laws that govern the motion of the constitutive particles of the system. It is not easy to estab­ lish precisely the dates of the birth of Statistical Mechanics.