The 'Euclidean approach to Quantum Gravity' was initiated 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. A 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 links with a Riemannian geometry. Since its inception the theory has been applied to a number of physical problems including the thermodynamic properties of black holes, quantum cosmology and the problem of the cosmological constant. This is a collection of survey lectures and reprints of some 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'.