This document discusses Fourier's law of heat conduction and the heat equation. It begins by recapping one-dimensional steady-state conduction and then discusses applying Fourier's law to different geometries. It derives the general heat conduction equation and describes how to write it for Cartesian, cylindrical, and spherical coordinate systems. Special cases of the heat equation like steady-state, no heat generation, and transient conditions are also covered. The document concludes by discussing the necessary boundary and initial conditions required to solve the heat equation.