  We give a full classification of general affine connections on Galilei
manifolds in terms of independently specifiable tensor fields. This generalises
the well-known case of (torsional) Galilei connections, i.e. connections
compatible with the metric structure of the Galilei manifold. Similarly to the
well-known pseudo-Riemannian case, the additional freedom for connections that
are not metric-compatible lies in the covariant derivatives of the two tensors
defining the metric structure (the clock form and the space metric), which
however are not fully independent of each other.
