Part one of this paper presents a method for measuring seismic velocities and transverse isotropy in rocks using a single core plug. This method saves at least two-thirds of the time for preparing core samples and measuring velocities in transversely isotropic (TI) rocks. Using this method, we have measured velocity and anisotropy of many shale and reservoir rocks from oil and gas fields around the world. We present some of the data in this paper, which include seismic velocity and anisotropy in 17 brine-saturated shale samples, 1 gas- and brine-saturated coal sample, 8 brine-saturated sands, 12 gas-saturated sands, 32 gas-saturated carbonate samples, and 25 brine-saturated carbonate samples. The results show that clays and fine layering in sedimentary rocks are the main causes of seismic anisotropy. Very little intrinsic anisotropy exists in unfractured reservoir rocks such as sands, sandstones, and carbonates under reservoir conditions. In contrast, all shales were found seismically anisotropic: anisotropy ranges from 6% to 33% for P-waves and from 2% to 55% for S-waves. The magnitude of shale anisotropy seems to decrease exponentially with increasing porosity. At present, the magnitude of shale anisotropy cannot be predicted accurately from other data without laboratory measurements. This paper also presents some best practices for laboratory measurements of shale velocity and anisotropy.