The increase of entropy was regarded as perhaps the most perfect and unassailable law in physics and it was even supposed to have philosophical import. Einstein, like most physicists of his time, regarded the second law of thermodynamics as one of the major achievements of the field, and it entered his work in several ways. The essence of the second law is the statement that all processes can be quantified by an entropy function whose increase is a necessary and sufficient condition for a process to occur. As a fundamental physical law no deviation, however tiny, is permitted and its consequences are far-reaching. Current wisdom regards the second law as a consequence of statistical mechanics but the entropy principle, which was discovered before statistical mechanics was invented, ought to be derivable from a few logical principles without recourse to Carnot cycles, ideal gases and other assumptions about such things as 'heat', 'hot' and 'cold', 'temperature', 'reversible processes', etc. Like conservation of energy (the ``first'' law), the existence of a law so precise and so model-independent must have a logical foundation that is independent of the details of the constitution of matter. In this lecture the foundations of the subject and the construction (with J. Yngvason) of entropy from a few simple principles will be presented. (No previous familiarity with the subject is required.) A summary can be found in: "A Guide to Entropy and the Second Law of Thermodynamics", Notices of the Amer. Math. Soc. vol 45 571-581 (1998). http://www.ams.org/notices/199805/lieb.pdf. arXiv math-ph/9805005 This paper received the American Mathematical Society 2002 Levi Conant prize for ``the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding five years''. A Fresh Look at Entropy and the Second Law of Thermodynamics, Physics Today {\bf 53}, 32-37 (April 2000). arXiv math-ph/0003028