All spacetimes beyond Einstein (Obergurgl Lectures)
  Which geometries on a smooth manifold (apart from Lorentzian metrics) can serve as a spacetime structure? This question is comprehensively addressed from first principles in eight lectures, exploring the kinematics and gravitational dynamics of all tensorial geometries on a smooth manifold that can carry predictive matter equations, are time-orientable, and allow to distinguish positive from negative particle energies. 
Frederic P. Schuller
gr-qc hep-th math-ph math.MP