The study of the soft x-ray spectrum affords, in principle, a unique method of measuring in a single experiment the density-of-states curve of a metal. Part I gives an elementary introduction to the theory of the band structure of metals and indicates how x-ray spectra can yield information about this structure. Certain features of the emission spectra can usually be identified with theoretically predicted phenomena. The Fermi edge can be identified, often without difficulty. Good agreement is generally obtained between the calculated widths of emission bands and those measured experimentally.