Analysis

On the Atiyah-Singer Index Theorem - An overview of the Atiyah-Singer Index Theorem that places the result in historical and mathematical context. [PDF]
http://www.abelprisen.no/nedlastning/2004/popular_english_2004.pdf

Advanced Calculus and Analysis - Lecture notes from the University of Aberdeen for a first course in Analysis.
http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/notes.html

Working Group on Generalized Convexity - An interdisciplinary group of scholars from operations research, economics, engineering, applied sciences, mathematics, statistics, among others, with an interest in generalizations of the classical concept of a convex function.
http://www.ec.unipi.it/~genconv/

An Introduction to the Gauge Integral - Discusses the properties of an alternative integration theory, and its relationship with the Riemann and Lebesgue integrals.
http://www.math.vanderbilt.edu/~schectex/ccc/gauge/

The International Society for Analysis, its Applications and Computation (ISAAC) - Established in 1994 to promote and advance analysis, its applications, and its interaction with computation. Meetings, lists.
http://mathisaac.org/

Computability and Complexity in Analysis Network - CCA Net aims to provide a central location for collecting information useful to researchers working in the field.
http://www.informatik.fernuni-hagen.de/import/cca/

Harmonic Analysis - Maintained by Terence Tao, UCLA. Lists events, personal pages, preprints, research groups, other links.
http://www.math.ucla.edu/~tao/harmonic/

The Nrich Maths Project Cambridge: Fractional Calculus I - Using the gamma function, a definition of integration and differentiation performed a fractional number of times is presented.
http://www.nrich.maths.org/public/viewer.php?obj_id=1365&part=index&refpage=monthindex.php