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Lecture I Attempts to relate the navier-stokes equations to turbulence.- Appendix to Lecture I: Bifurcations, semiflows, and navier-stokes equations.- Lecture II Theories of turbulence.- Lecture III Dynamical systems and turbulence.- Lecture IV A phenomenonological theory for the computation of turbulent shear flows.- Lecture V Fractals and turbulence: Attractors and dispersion.- Lecture VII The structure of lorenz attractors.- Appendix to Lecture VII: Computer pictures of the Lorenz attractor.- Lecture VIII a model for couette flow data.- Two attempts at modeling two-dimensional turbulence.