The results of energy band calculations for all of the alkali metals Li, Na, K, Rb, and Cs, obtained using the quantum defect method and the Green's function method, are reported for points of low symmetry within the Brillouin zone as well as for the usual points of high symmetry. Definite trends in the band structure are revealed through the alkali metal series and as a function of lattice constant. The Fermi surfaces of Li and Cs are the most distorted by bulges in the [110] directions, while those of Na and K are nearly spherical; the corresponding gaps (${N}_{1}\ensuremath{-}{N}_{{1}^{\ensuremath{'}}}$) at equilibrium at 0\ifmmode^\circ\else\textdegree\fi{}K are (in rydbergs): Li, +0.209; Na, +0.018; K, -0.037; Rb, -0.063; Cs, -0.088. Except for Na the gaps and distortion increase significantly in magnitude with decreasing lattice constant. However the Fermi surface of Li is found not to contact the zone face even under substantial pressure, while contact occurs for Cs at a slight compression. Excited bands are also given; there is a pronounced trend for $d$ states to fall increasingly lower relative to $s$, $p$, and $f$ states in the sequence Li to Cs, and for $p$ states to rise in this sequence relative to $s$ and $f$ states. Detailed comparisons are given with calculations by Callaway, Brooks, Schlosser, Allen, and others. These comparisons support the view that the significant features of these band structures are not very sensitive to uncertainties in the crystal potential.