Preliminaries and Notation. - Classical Approximation Theorems. - Operational Calculus in One Variable. - Differential Forms. - The -Operator. - The Equation. - The Oka-Weil Theorem. - Operational Calculus in Several Variables. - The Šilov Boundary. - Maximality and Radó's Theorem. - Maximum Modulus Algebras. - Hulls of Curves and Arcs. - Integral Kernels. - Perturbations of the Stone?Weierstrass Theorem. - The First Cohomology Group of a Maximal Ideal Space. - The -Operator in Smoothly Bounded Domains. - Manifolds Without Complex Tangents. - Submanifolds of High Dimension. - Boundaries of Analytic Varieties. - Polynomial Hulls of Sets Over the Circle. - Areas. - Topology of Hulls. - Pseudoconvex sets in ?n. - Examples. - Historical Comments and Recent Developments. - Solutions to Some Exercises. Language: English