Statistical mechanics underlies nearly every aspect of mechanical engineering: it explains thermodynamics, underlies fluid mechanics, provides constitutive laws for continuum mechanics, and gives the foundations to transport phenomena near and far from equilibrium. This course develops the basic ideas of statistical mechanics by way of its manifold applications across science and engineering. We will focus particular attention on emergent properties. Topics include temperature, equilibrium, ergodicity, entropy, phase transitions, and symmetries. We will develop these ideas in the contexts of transport, material properties, fluid mechanics, and emerging areas of engineering including active matter.