A partial-wave analysis of K⁺-nucleon scattering has been performed. Energy-dependent and energy-independent solutions for the isoscalar and isovector amplitudes are generated by fitting data with a chi-squared minimization technique. The isoscalar amplitudes extend to a K⁺ incident lab kinetic energy of 1100 MeV; the isovector amplitudes extend to 2650 MeV. Due to the lack of a neutron target and scarcity of isoscalar data, K⁺-deuteron inelastic and elastic data are utilized in the analysis. The theories which incorporate the K⁺-deuteron data are fixed-scatterer, single-scattering impulse approximations. Two different techniques are employed to find preliminary energy-dependent isoscalar solutions for the scattering amplitudes. The first technique involves initializing to two different single-energy solutions of previous studies. The second technique consists of utilizing the energy-dependent parametrization to fit successively larger bins of data, starting from zero energy, until the entire energy range is covered. Two solutions result from these investigations since one of the solutions from the first technique agrees with the solution from the second technique. The partial-wave amplitudes are discussed. Resonance pole positions and scattering lengths are extracted from each solution and compared with predictions from theories and other analyses. Also, observables from each solution are compared and experiments are suggested to further refine the determination of the K⁺N partial-wave amplitudes. / Ph. D.