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After a short introduction to the characteristic geometry underlying weaklyhyperbolic systems of partial differential equations we review the notion ofsymmetric hyperbolicity of first-order systems and that of regularhyperbolicity of second-order systems. Numerous examples are provided, mainlytaken from nonrelativistic and relativistic continuum mechanics.Comment: 12 pages, uses svmult.cls style file, expanded version of lecture  given at 319th WE-Heraeus Seminar on "Mathematical Relativity: New Ideas and  Developments

Concepts of Hyperbolicity and Relativistic Continuum Mechanics