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The course will begin with a brief recap of low-Reynolds number hydrodynamics and the analytical foundations for the study of pair-level particle interactions in a Newtonian solvent. Extension to many-body interactions will be covered in detail, with an introductory overview of computational methods. Brownian motion, thermodynamic forces, and other interparticle forces will be discussed, and various approaches for theoretical modeling will be covered, including Fokker-Planck / Smoluchowski analysis and Langevin analysis. Theoretical and computational modeling of material properties via averaging techniques will be studied, in the context of micromechanical and continuum models. Landmark results in the microrheology and rheology of complex fluids will be covered, including sedimentation, non-Newtonian rheology (including shear thinning and thickening; viscoelasticity and memory behaviors; yield-stress behavior; glassy aging; diffusion; normal stress differences).