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I'm interested right now to learn more about the tautological bundle over the Grassmann manifold $G_{k,n}(\mathbb{R})$, but I'm currently having trouble finding the appropriate texts to check out. There's obviously Wikipedia, and I've also found a link to John Milnor's Characteristic Classes, but I'm looking for something that's a little more pointed and directed (an article or two would be ideal).

My main interest in this stemmed from Milnor's lecture (go to 27:00) at Cornell where he described how this bundle space can be used as a classification space for tangent bundles.

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    I would give milnor stasheff another shot. The stuff about the grassmannians is really at the beginning, and really well written. – 2017-02-23

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Longer than an article, but still a good point of reference, is Hirsch's "Differential Topology". Chapter 4 on vector bundles includes classification theorems relating vector bundles to maps into Grassmannians.

Be warned, this book has tons of insidious errata. A partial list has been compiled here.

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    Thank you! This will be a great place for me to start. – 2017-02-22