For beginers, any suggestions?
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6$\begingroup$ How about the book references in the wikipedia page? en.wikipedia.org/wiki/Building_%28mathematics%29 $\endgroup$– j.c.Commented Aug 31, 2011 at 1:55
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$\begingroup$ In case your motivation is the study of arithmetic groups, then Serre's "Trees" would be an excellent start! If not, then also, but might want to leave it at chapter 1. $\endgroup$– Peter ArndtCommented Dec 6, 2011 at 20:25
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6 Answers
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A good reference is Ken Brown and Peter Abramenko's "Buildings" (there is also the first edition freely available at http://www.math.cornell.edu/~kbrown/buildings/). Otherwise, you may want to look at Tits' "Reductive groups over local fields" from the Corvallis 1979 proceedings (see Corvallis 1979 proceedings).
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In my opinion, the beginner would find the following very helpful:
MacDonald's book, spherical functions on a group of p-adic type (out of print)
Joseph Rabinoff's senior thesis at Harvard. It's a very readable exposition.
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5$\begingroup$ Rabinoff's thesis is indeed well written. Nice reference. $\endgroup$ Commented Oct 3, 2011 at 23:47
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4$\begingroup$ The link seems broken; here is another one: math.stanford.edu/~rabinoff/misc/building.pdf $\endgroup$ Commented Jun 30, 2017 at 0:22
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1$\begingroup$ I second Rabinoff's thesis, it is incredible especially as an introduction to the subject $\endgroup$ Commented Dec 13, 2018 at 18:11
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3$\begingroup$ Here is another link for Rabinoff's thesis: services.math.duke.edu/~jdr/papers/building.pdf $\endgroup$ Commented Nov 8, 2022 at 15:48
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Since this question was asked, Brent Everitt wrote A (very short) introduction to buildings. It comes with many pictures to help you visualize them, and a long list of pointers to where to find out more about each aspect in the literature.
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Tits' original lecture notes from 1974 (Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, 386, Springer-Verlag) can still serve as a very good introduction to the subject.
Another excellent reference (and not as voluminous as Abramenko--Brown) is the pair of books by Richard Weiss: "The structure of spherical buildings" and "The structure of affine buildings" (both published by Princeton University Press).
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A book suited well for beginners on the subject is "Lectures on buildings" by Mark Ronan.
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Just a comment (sorry but I can't comment yet) : if you want not to 'waste' to much time, you should tell people what kind of specific problems you want to work in; as far as I remember, Tits' book (spherical buildings) is essentially combinatorial, so for instance you can read it without much knowledge of algebraic groups. But if you intend to solve problems in that direction, then indeed the book of Brown for instance is better direction. I'm not a specialist but I hope that people will give you more infos on the references they recommend.