Loosely speaking, entropy measures the degree of disorder in a thermodynamic system. The second law of thermodynamics states that, due to the random thermal motion, the entropy of a closed system always increases and reaches its maximum when the system comes to equilibrium. In the first half of this course, we will examine the foundations of thermodynamics, and, in particular, the law of entropy increases. Special attention will be paid to the objections raised against this statement after its introduction in the 1850s by Clausius and Kelvin. Topics such as Maxwell's demons, irreversibility, Poincaré theorem, etc. will be reviewed, as well as some very recent advances in the field, such as Jarzinsky's identity. The second part of the course is intended to serve as an introduction to non-equilibrium statistical physics. Some counterintuitive non-equilibrium phenomena, where noise actually assists in increasing the degree of order in the system, will be introduced and discussed.