  Related to the classical Ashtekar Hamiltonian, there have been discoveries
regarding new classical actions for gravity in (2+1)- and (3+1)-dimensions, and
also generalizations of Einstein's theory of gravity. In this review, I will
try to clarify the relations between the new and old actions for gravity, and
also give a short introduction to the new generalizations. The new
results/treatments in this review are: 1. A more detailed constraint analysis
of the Hamiltonian formulation of the Hilbert- Palatini Lagrangian in
(3+1)-dimensions. 2. The canonical transformation relating the Ashtekar- and
the ADM-Hamiltonian in (2+1)-dimensions is given. 3. There is a discussion
regarding the possibility of finding a higher dimensional Ashtekar formulation.
There are also two clarifying figures (in the beginning of chapter 2 and 3,
respectively) showing the relations between different action-formulations for
Einstein gravity in (2+1)- and (3+1)-dimensions.
