This thesis presents results on the description of plasma waves in terms of wavepackets. The wave field is decomposed into a distribution of wavepackets in a space of position, wavevector, time, and frequency. A complex structure joining each pair of Fourier conjugate variables into a single complex coordinate allows the efficient derivation of equations of motion for the phase space distribution by exploiting its analytic properties. The Wick symbol calculus, a mathematical tool generalizing many convenient properties of the Fourier transform to a local setting, is used to derive new exact phase space equations which maintain full information on the phase of the waves and include effects nonlocal in phase space such as harmonic generation. A general purpose asymptotic expansion of the Wick symbol product formula is used to treat dispersion, refraction, photon acceleration, and ponderomotive forces. Examples studied include the nonlinear Schrödinger equation, mode conversion, and the Vlasov equation. The structure of partially coherent wave fields is understood in terms of zeros in the phase space distribution caused by dislocations in its complex phase which are shown to be correlated with the field entropy. Simulations of plasma heating by crossing electron beams are understood by representing the resulting plasma waves in phase space. The local coherence properties of the beam driven Langmuir waves are studied numerically.
