This course will introduce the basic objects of study in harmonic analysis on reductive groups and Lie algebras over local fields: orbital integrals, their Fourier transforms (in the Lie algebra case) and characters of irreducible representations (in the group case). The emphasis will be on p-adic fields and the Lie algebra case (to which the group case can often be reduced using the exponential map). Some of the main theorems involving these objects will be discussed: Howe's finiteness theorem; Shalika germs, the local character expansion and its Lie algebra analog; local integrability of Fourier transforms of orbital integrals; and the Lie algebra analog of the local trace formula.