PSPLINE is a collection of Spline and Hermite interpolation tools for 1D, 2D, and 3D datasets on rectilinear grids. Spline routines give full control over boundary conditions, including periodic, 1st or 2nd derivative match, or divided difference-based boundary conditions on either end of each grid dimension. Hermite routines take the function value and derivatives at each grid point as input, giving back a representation of the function between grid points. Routines are provided for creating Hermite datasets, with appropriate boundary conditions applied. The 1D spline and Hermite routines are based on standard methods; the 2D and 3D spline or Hermite interpolation functions are constructed from 1D spline or Hermite interpolation functions in a straightforward manner. Spline and Hermite interpolation functions are often much faster to evaluate than other representations using e.g. Fourier series or otherwise involving transcendental functions.