I did say I had an interesting mix of things to review, didn't I?
Though it doesn't say, I think this one is an adaptation of a thesis. It has that feel. The language isn't super-elegant, but it's very clear, and easy to understand even with little knowledge of astronomy or Lakota culture.
Probably the number one best thing in it, which I'd scan if I had a scanner, is a star map with both Lakota and Greek constellations indicated. There's very little correspondence between the two (in that they don't even line up, let alone represent the same things), but there are certain features which are important to both. These include Cygnus, the square of Pegasus, Orion, and the Dipper; I'd venture that these features are intrinsically noticeable and will never not give the impression of being connected. Neat.
Anyway, on to content ...
It was very important which part of the sky the sun was in. As the sky and earth were understood to reflect each other, the sun is seen to travel through a landscape of the sky, which is a mirror of the landscape of the earth. Thus, the people travel through the land, following the path set by the sun. It was vital, in the period between spring equinox and summer solstice to travel from winter camps (matching the Dried Willow constellation; the time and place at which the willow was harvested) to Devil's Tower (matching Bear's Lodge constellation; legends concerning the origin of Devil's Tower involve a bear.)
In star maps, the symbol used to represent a star is an hourglass shape, meaning that the star is seen as the part of a vortex, a connection between the sky and the earth. The shape of the tipi, and the Sun Dance, have also both been described as the bottom part of that vortex. There is believed to be a constant connection between the two worlds.
So -- detailed observations, used reliably for timekeeping, for at least 3000 years. And usually gets about half a sentence in your average astronomy textbook's history chapter.