This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general functional equations. It guides the reader from the ''basics'' to the current state-of-the-art level of the field, describes important problems and directions for future research, and highlights methods. The analysis includes numerous exercises and applications to the modelling of physical and biological phenomena.

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