Legendre Transform, conjugate functions and Quasi-(Concavity/Convexity)

These are some helpful links to better understand conjugate functions:

http://maze5.net/?page_id=733
https://en.wikipedia.org/wiki/Legendre_transformation
http://www.onmyphd.com/?p=legendre.fenchel.transform
http://physics.stackexchange.com/questions/4384/physical-meaning-of-legendre-transformation
http://jmanton.wordpress.com/2010/11/21/introduction-to-the-legendre-transform/

Quasiconcavity and Quasiconvexity
http://www.economics.utoronto.ca/osborne/MathTutorial/DFI.HTM#s:levelcurves