Many sets arising in such disparate branches of mathematics as geometry, complex analysis, mathematical physics and symmetries of differential equations share a common spatial structure - they are manifolds. Locally they appear like Euclidean spaces but they may have a very different global structure. The local Euclidean character of manifolds enables techniques of calculus and analysis to be transferred to them. This can give us information about the structure of manifolds and maps between them and provide the appropriate setting for many non-linear physical problems. In MATH 455 basic ideas of differential topology are introduced and further topics may include singularities, degree theory, dynamical systems and differential forms.
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