When I was a student some 30 years ago, I attended a couple of courses which, among the various topics, discussed liquid crystals (they were 3rd year courses). The books I'm going to list here are those I used at the time to prepare the exams: In general, they are quite theoretical, thoroughly discussing thermodynamics, ordering and phase transitions of liquid crystals, but they may be a bit outdated on the applications. Some background on mean-field theories and on the theory of elasticity can be useful.
[1] E. B. Priestley, P. J. Woitowicz, P. Sheng (eds.), Introduction to liquid crystals, Plenum Press, 1979. Note: This is certainly the less theoretical among the listed books, and the first chapter provides a smooth introduction to the topic.
[2] S. Chandrasekhar, Liquid crystals, Cambridge University Press, 2nd edition, 1992.
[3] P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon Press, 2nd edition, 1995. Note: I don't have specific recollections on this, but it's from one of the major contributors to the field and probably quite comprehensive,