The main stimulus for preparing this new edition was the lively development of the subject
since the publication of the first edition in 2011. I have tried to incorporate the new results as …

Given an irreducible affine algebraic variety X of dimension n≥ 2, we let SAut (X) denote the
special automorphism group of X, that is, the subgroup of the full automorphism group Aut …

In this paper we expose the impact of the fundamental discovery, made by Erik Andersen
and László Lempert in 1992, that the group generated by shears is dense in the group of …

We study hypersurfaces of C^ n+ 2 _ ̄ x, u, v given by equations of form UV= P (̄ X) where
the zero locus of a polynomial p is smooth reduced. The main result says that the Lie …

An affine variety X of dimension≥ 2 is called flexible if its special automorphism group SAut
(X) acts transitively on the smooth locus Xreg. Recall that SAut (X) is the subgroup of the …

In this survey of the Andersén–Lempert theory we present the state of the art in the study of
the density property (which means that the Lie algebra generated by completely integrable …

We prove that a Stein manifold of dimension d admits a proper holomorphic embedding into
any Stein manifold of dimension at least 2 d+ 1 satisfying the holomorphic density property …

We introduce the notion of algebraic volume density property for affine algebraic manifolds
and prove some important basic facts about it, in particular that it implies the volume density …

We present modified versions of existing criteria for the density property and the volume
density property of complex manifolds. We apply these methods to show the (volume) …

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