  These notes are written up after my lectures at the University of Pittsburgh
in March 2014 and at Tsinghua University in May 2014. My objective is the
$\infty$-Laplace Equation, a marvellous kin to the ordinary Laplace Equation.
The $\infty$-Laplace Equation has delightful counterparts to the Dirichlet
integral, the Mean Value Theorem, the Brownian Motion, Harnack's Inequality and
so on. It has applications to image processing and to mass transfer problems
and provides optimal Lipschitz extensions of boundary values. My treaty of this
"fully non-linear" degenerate equation is far from complete and generalizations
are deliberately avoided.
