  These notes are self-contained, with the first 7 chapters used in a
one-semester course with recommended texts by Wald, by Misner, Thorne and
Wheeler, and by Schutz. In its treatment of topics covered in these standard
texts, the presentation here typically includes steps skipped in Wald or MTW.
Treatments of gravitational waves, particle orbits in black-hole backgrounds,
the Teukolsky equation, and the initial value equations are motivated in part
by the discoveries of gravitational waves from the inspiral and coalescence of
binary black holes and neutron stars, advances in numerical relativity, and the
expected LISA space-based observatory. The notes begin with a detailed
presentation of special relativity with a geometrical orientation, starting
with with time dilation and length contraction and including relativistic
particles, fluids, electromagnetism, and curvilinear coordinates. Chaps. 2-5
cover curvature, the Einstein equation, relativistic stars, and black holes.
Chap. 6, on gravitational waves, includes a discussion of detection and noise.
Chap. 7 is a brief introduction to cosmology, deriving the metrics of
homogeneous isotropic space, the equations governing a universe with matter,
radiation and vacuum energy, and their solutions, and discussions of the
cosmological redshift and on using gravitational waves to measure the Hubble
constant.
  Chap. 8, on the initial value problem, has a section on the form of the
equations used in numerical relativity. The Newman-Penrose formalism and the
Teukolsky equation are covered in Chap. 9. Following that is a chapter on
black-hole thermodynamics and a final chapter on the gravitational action and
on conserved quantities for asymptotically flat spacetimes, using Noether's
theorem. An appendix covers forms, densities, integration, and Cartan calculus.
