This course will focus on the relationships between the cellular microstructure and the nonlinear mechanical behavior of liquid and solid foams, as well as foam-like biological and synthetic materials. Consequently, this survey of foam mechanics will explore numerous topics in applied mechanics ranging from traditional fluid mechanics to solid mechanics. Theoretical analysis, numerical simulations, and experiments will be used to unravel the complex relationships between cell-level structure, local deformation mechanisms, and macroscopic mechanical behavior. The cells in liquid foams, such as soap froth, are polyhedral gas bubbles separated by thin liquid films that are stabilized against rupture by surfactants. Many commercially important cellular solids, such as polymer, food, and metal foams, are formed when liquid foams solidify into structures that can have open or closed cells. The growth of spherical gas bubbles in a liquid and their evolution to form the polyhedral cells in low-density foam are key features of foam manufacturing processes, and illustrate the interplay between the mechanics of liquid and solid foams. The cell-level architecture of low-density foams can be viewed as space-filling polyhedra, forming regular or random networks of surfaces and edges. Similar networks are characteristic of biological materials, such as trabecular bone, the cytoskeleton, and cells in animal tissues such as the eye of the Drosophila fruit fly. Liquid foams are used in firefighting, mineral ore separation, drilling fluids and mobility control in the petroleum industry, as well as a wide range of consumer products, foods and beverages. Natural and synthetic cellular solids are lightweight materials with unique and advantageous combinations of properties involving stiffness- and strength-to-weight ratio, energy absorption, thermal insulation and acoustics, all of which can be tuned by controlling density and cell morphology. Despite significant progress in understanding foam rheology and mechanics over the last few decades, the complex nonlinear phenomena that occur at all length scales remain poorly understood. Whether the structure is two-dimensional and ordered or three-dimensional and highly disordered the fluid mechanics and solid mechanics is very challenging when taking a micromechanical point of view. For solid foams connecting the microstructure and the mechanical properties of the base material to the macroscopic behavior remains a challenge. Models involving idealized ordered microstructures, such as the Kelvin foam, and realistic random microstructures with different cell sizes will be presented, and the strengths and weaknesses in predicting all aspects of mechanical behavior will be discussed. Taken as a whole, the participants will be presented with the state of the art of the mechanics of liquid and solid foams and will be exposed to many open questions. The broad course topics are: cell-level foam structure (including a tutorial on Surface Evolver simulations), rheology and aging of liquid foam, and the mechanics of solid foams and biological cellular materials. Both liquid and solid foams exhibit linear elasticity, yielding and plasticity, and the onset and propagation of instabilities. The target audience for this course includes PhD students and postdocs in engineering, physics, and materials science, as well as young and senior researchers in academia and industry.