In this volume the author studies noncommutative domains $mathcal{D}_fsubset B(mathcal{H})^n$ generated by positive regular free holomorphic functions $f$ on $B(mathcal{H})^n$, where $B(mathcal{H})$ is the algebra of all bounded linear operators on a Hilbert space $mathcal{H}$. Table of Contents: Introduction; Operator algebras associated with noncommutative domains; Free holomorphic functions on noncommutative domains; Model theory and unitary invariants on noncommutative domains; Commutant lifting and applications; Bibliography. (MEMO/205/964)

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