The Euclidean approach to Quantum Gravity was initiated almost 15
years ago in an attempt to understand the difficulties raised by
the spacetime singularities of classical general relativity which
arise in the gravitational collapse of stars to form black holes
and the entire universe in the Big Bang. An important motivation
was to develop an approach capable of dealing with the nonlinear,
non-perturbative aspects of quantum gravity due to topologically
non-trivial spacetimes. There are important links with a Riemannian
geometry. Since its inception the theory has been applied to a
number of important physical problems including the thermodynamic
properties of black holes, quantum cosmology and the problem of the
cosmological constant. It is currently at the centre of a great
deal of interest.This is a collection of survey lectures and
reprints of some important lectures on the Euclidean approach to
quantum gravity in which one expresses the Feynman path integral as
a sum over Riemannian metrics. As well as papers on the basic
formalism there are sections on Black Holes, Quantum Cosmology,
Wormholes and Gravitational Instantons.
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