Statistical Mechanics is a fundamental bedrock of both classical and quantum physics. We cannot possibly hope to know all the details of what happens to all 10²³ atoms or molecules making up a sample of macroscopic size - and why should we try to garner so much information? Many of the measurable properties of the world outside us are really averages of microscopic events. The pressure of a gas on the walls of a container is made up of the impact of a vast number of collisions of individual molecules with the wall and we observe the average effect of these collisions as the pressure. In this module we shall study how such an averaging is carried out by means of both time averaging and ensemble averaging. Clearly there may be no point in calculating an average value to represent a typical value of a measurable physical quantity if fluctuations about that average are very large, and so we shall also study the fluctuations of the system about these averages and see how the fluctuations themselves can be important in determining measurable quantities such as specific heats. There are subtle differences between classical systems and those governed by the laws of quantum mechanics and this module will explore these differences and also discuss how the quantum statistics of the particles making up a macroscopic system influence the thermal properties of the system. Many applications of these ideas from condensed matter physics, astrophysics and radiation physics will be given. Finally, if time permits, we shall mention the phenomenon of Bose-Einstein condensation which lies beneath an understanding of superfluidity and superconductivity and which has only recently been realised experimentally in atom traps and has led to the award of the Nobel Prize to Wolfgang Ketterle, Carl Wieman and Eric Cornell in 2001.