SHTOOLS performs (among others) spherical harmonic transforms and reconstructions, rotations of spherical harmonic coefficients, and multitaper spectral analyses on the sphere. The package accommodates any standard normalization of the spherical harmonic functions ("geodesy" 4π normalized, Schmidt semi-normalized, orthonormalized, and unnormalized), and either real or complex spherical harmonics can be employed. Spherical harmonic transforms are calculated by exact quadrature rules using either (1) the sampling theorem of Driscoll and Healy (1994) where data are equally sampled (or spaced) in latitude and longitude, or (2) Gauss-Legendre quadrature. A least squares inversion routine for irregularly sampled data is included as well. The Condon-Shortley phase factor of (-1)m can be used or excluded with the associated Legendre functions. The spherical harmonic transforms are accurate to approximately degree 2800, corresponding to a spatial resolution of better than 4 arc minutes. Routines are included for performing localized multitaper spectral analyses and standard gravity calculations, such as computation of the geoid, and the determination of the potential associated with finite-amplitude topography. The routines are fast. Spherical harmonic transforms and reconstructions take on the order of 1 second for bandwidths less than 600 and about 3 minutes for bandwidths close to 2800.