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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a piecewise linear function is a piecewise-defined function whose pieces are linear. The notion of a piece wise linear function makes sense in several different contexts. Piecewise linear functions may be defined on n-dimensional Euclidean space, or more generally any vector space or affine space, as well as on piecewise linear manifolds, simplicial complexes, and so forth. In each case, the function may be real-valued, or it may take values from a vector space, an affine space, a piecewise-linear manifold, or a simplicial complex. (In these contexts, the term linear does not refer solely to linear transformations, but to more general affine linear functions.)