An undergraduate student of mine is interested in writing a "senior" thesis on the topology of Lie groups. Let $G$ be a simply connected compact Lie group and $T$ a maximal torus. One way of calculating $\pi_2(G)$ and $\pi_3(G)$ proceeds via the Bott and Samelson construction of a perfect Morse function on $G/T$ (Perhaps the more standard way is via Iwasawa decompositions and the description of $G/T$ as a complex manifold, but my student says he prefers "geometry" to "algebra").

Bott and Samelson's papers are of course wonderful but aside from being rather vintage, they are research papers and they discuss a lot of applications to loop spaces, whose infinite dimensional nature I think would be intimidating for this student. I am therefore looking for a reference that I can give to my student that discusses this construction in a fairly "hands-on" and friendly fashion and has relatively complete proofs up to perhaps isolating one or two facts from Lie theory (say about the $\operatorname{Ad}$ representation or the Weyl group). Any suggestions?

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