17 pages of notes for an independent study by Christopher Pilman, in addition to the previous sets of differential geometry notes [1984, 1991], with several pages on the Lie derivative copied from Introduction to Cosmological Models 2.
The rotations in the plane are used to motivate a general 1-parameter group of transformations, using the exponential map, then specializing back to the rotations showing the relation to the matrix generators and matrix transformation. Comoving coordinates are found for this example. Then dragging and the Lie derivative are introduced. Then the relationship between the rotation generators and linear and angular momentum is discussed. Next r-parameter groups and rotations of space, then boosts of 2-d Minkowski spacetime, and the generators of the 4-d Lorentz group. Finally the Lie derivative and isometry actions are touched upon, with a final exercise.