The recently completed book, Harmonic Measure, with J. Garnett, devotes the first four chapters to classical material suitable for a second year course (graduate) in complex analysis, while the last four chapters cover recent advances on Bloch functions, Brennan's conjecture, harmonic measure in infinitely connected domains, rectifiability and other topics in geometric function theory.

Selected bibliography

The Loewner Differential Equation and Slit Mappings, with S. Rohde, J. Amer. Math. Soc. 18 (2005), no. 4, 763-778.

"Harmonic Measure", with J. Garnett, Cambridge University Press, June 2005, 587pp.

A Lipschitz Decomposition of Minimal Surfaces, with J. Garnett and P. Jones, J. Diff. Geo. 35 (1992), 659-673.

Frequency Domain Design and Analytic Selections, with J. W. Helton, Indiana Univ. Math. J. 39 (1990), 157-184.

On a Sharp Inequality Concerning the Dirichlet Integral, with S.-Y.A. Chang, Amer. J. Math. 107 (1985), 1015-1033.

Critical Points of Green's Function, Harmonic Measure, and the Corona Problem, with P. Jones, Ark. för Mat. 23 (1985), 281-314.

Subalgebras of L^∞ containing H^∞, Acta Math. 137 (1976), 91-98.

Zipper, Fortran programs for numerical computation of conformal maps, and C programs for X-11 graphics display of the maps. Sample pictures, Fortran and C code available at URL: http://www.math.washington.edu/~marshall/zipper.html