We review the structure of atoms to describe allowed intra-atomic electronic transitions following dipole selection rules. Inner shell ionization is followed by characteristic X-ray emission or non-radiative de-excitation processes leading to Auger electrons that involve three atomic levels. Photon incidence also results in characteristic photoelectron emission, reflecting the energy distribution of the electrons in the solid. We present details of laboratory and synchrotron sources of X-rays, and discuss their detection by wavelength or energy-dispersive spectrometers, as well as microanalysis with X-ray (XRF), or electron (EPMA) incidence. Characteristic X-ray intensities are quantified in terms of composition using corrections for atomic number (Z), absorption (A), and fluorescence (F). Electron detectors use electrostatic or magnetic dispersing fields; two common designs are electrostatic hemispheric or mirror analyzers. Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS), used for surface analysis, require ultra-high vacuum. AES is a weak signal, best resolved in a derivative spectrum, shows sensitivity to the chemical state and the atomic environment, provides a spatially-resolved signal for composition mapping, and can be quantified for chemical analysis using sensitivity factors. Finally, we introduce the basics of XPS, a photon-in, electron-out technique, discussed further in §3.