Abstarct: DKP equation is the special case of the first-order relativistic wave equations for arbitrary spin particles. DKP equation is a Dirac-Like equation which describes spin0 and spin-1 particles. This equation is of great importance many areas of physics including cosmology, meson spectroscopy and nuclear hadron interactions. So the particles like photons, gluons, mesons, excitons, can be considered by DKP equation. In this thesis, we discussed about DKP theory. Then we have explained about the properties of DKP equation. Also we have studied DKP equation under of central and non-central potentials and investigate energy eigenvalues and eigenfunctions. Then we have considered the scattering of spin-zero and spin-one bosons in (1+1) dimension and obtained transmission and reflection coefficients and bound states of spin-zero and spin-one bosons. Also we have considered the scattering of spin-one bosons in (3+1) dimensions and introduced the phase shift.