Differential cross sections and vector analyzing powers have been measured for elastic and inelastic scattering of deuterons from 9Be, for the 9Be(d, p)10Be reactions leading to both bound and unbound states of 10Be, and for the 9Be(d, t)8Be and 9Be(p, d)8Be reactions to the ground and first-excited states of 8Be. A bombarding energy of 15 MeV was used for all of the measurements. Separate optical model and DWBA analyses of the elastic scattering and inelastic scattering to the 2.43 MeV level of 9Be, respectively, agree fairly well with the data, while a coupled-channels analysis of the combined data for elastic scattering and inelastic scattering to the 2.43 MeV level is much less successful. The transfer reaction data were analyzed with the DWBA, using resonance neutron form factors for the calculations on transitions to the unbound states in 10Be. For the most part, the (d, p) data are reproduced only at forward angles by the DWBA calculations. For the (d, t) reaction, rather good qualitative agreement with the data is obtained, in contrast with the (p, d) reaction, for which the agreement is poor. Spectroscopic factors and information on j-mixing in good agreement with the predictions of Cohen and Kurath are obtained for several of the transfer reactions. The transitions to the 2+ levels of 10Be at 5.958 and 7.542 MeV appear to proceed by processes other than simple stripping with ln = 1. A negative parity assignment is suggested for the 9.40 MeV level in 10Be.