Here are some references for the summer REU on rigidity of graphs:

• Asimow and Roth, "The Rigidity of Graphs", Transactions of the AMS 245 (1978), 279–289 (PDF). Basic results on local versus infinitesimal rigidity, and rigidity of complete graphs.
• Hendrickson, "Conditions for Unique Graph Realizations", SIAM J. Comput 21 (1992), 65–84 (Djvu, PDF).
• Hendrickson, "The molecule problem: Exploiting structure in global optimization" SIAM J. Optim. 5 (1995), no. 4, 835–857 (PDF).
• Connelly, "On generic global rigidity", DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 4 (1991), 147–155 (Djvu, PDF).
• Connelly, "Generic global rigidity", Discrete Comput. Geom. 33 (2005), 549–563 (PDF).
• Gortler, Healy, and Thurston, "Characterizing Generic Global Rigidity" (PDF).
• Connelly, "Tensegrities and global rigidity" (PDF).
• Singer and Cucuringu, "Uniqueness of Low-Rank Matrix Completion by Rigidity Theory".
• Connelly, "Rigidity and Energy", Inventiones Mathematicae 66 (1982), 11–33 (PDF).
• "The Not So Short Introduction to LaTeX", by Oetiker et al, is a good introduction to LaTeX. Despite the name, it is not very long.