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Infinitesimal analysis, once a synonym for calculus, is a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960s with the epithet “nonstandard”, infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. This book sets forth the basics of the theory, as well as up-to-date applications in, for example, functional analysis, optimization, and harmonic analysis.
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