BOOKS

Textbooks:

• Harriet Pollatsek,
  Lie Groups: A Problem-Oriented Introduction via Matrix Groups,
  MAA, 2009.
  An elementary introduction to matrix Lie groups.
  OSU owns an electronic copy of this book, which can be accessed here.
• Tevian Dray and Corinne A Manogue,
  The Geometry of the Octonions,
  World Scientific, 2015.
  An elementary introduction to the octonions and their use in describing certain symmetry groups.
  OSU owns an electronic copy of this book, which can be accessed here. (Most content is also available here.)

Other Books on Lie Groups/Lie Algebras:

• William Fulton and Joe Harris, Representation Theory: A First Course,
  Springer-Verlag, 1991.
  An excellent graduate mathematics text.
• Karin Erdmann and Mark J. Wildon, Introduction to Lie Algebras,
  Springer Verlag, 2006
  Suitable for advanced undergraduates; a somewhat easier read than Fulton & Harris.
  Online access is available through the OSU library.
• William M. Boothby, An Introduction to Differential Manifolds and Riemannian Geometry,
  Academic Press, 1975 (2nd edition: 1986; revised 2nd edition: 2002)
  A graduate-level introduction to differential geometry; discusses Lie groups and Lie algebras.
• Anthony Zee, Group Theory in a Nutshell for Physicists,
  Princeton University Press, 2016
  All of the essential math is here, with lots of details and applications to physics.