Dear all, A beta version of my new book "Synthetic Geometry of Manifolds" is available via my homepage, http://home.imf.au.dk/kock/ This book deals with some classical spaces in differential geometry, namely the "prolongation spaces" or "neighbourhoods of the diagonal". These spaces provides a natural way of describing some of the basic constructions in local differential geometry, and in fact, is an inviting gate to differential geometry, and also to some of those differential-geometric notions that exist in algebraic geometry. In the present text, the neighbourhoods of the diagonal are dealt with, and utilized, using the axiomatic method of synthetic differential geometry; this obviates many of those technical difficulties, which till now has made the use of these neighbourhoods rather uninviting. Some of the specific differential geometric theories dealt with here are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, harmonic maps. Anders Kock