I think there are several papers that can give you a good introduction. The seminal papers of Parry and Rényi have been already mentioned as well as Dajani-Kraikaamp's book. I think that Nikita Sidorov's paper [Arithmethic Dynamics][1] is very useful as well as his [lecture notes][2]. Also Dajani&Kraaikamp's paper [From Greedy to Lazy expansions and their driving dynamics][3] is relevant as well as Komornik's paper [Expansions in noninteger bases][4].

Now, [Simon Baker's][5] and [Derong Kong's][6] papers contain very well written brief introductions to the topic. 

**EDIT**  I found these notes today. 
[http://wisdyn.math.uni-bremen.de/betabremen.pdf][7]
[http://wisdyn.math.uni-bremen.de/Lingmin.pdf][8]   


  [1]: http://www.maths.manchester.ac.uk/~nikita/ad.pdf
  [2]: http://www.maths.manchester.ac.uk/~nikita/qmul-2010.pdf
  [3]: http://dutiosc.twi.tudelft.nl/~cork/monthly.pdf
  [4]: http://www.ams.org/mathscinet/search/publdoc.html?agg_year_2011=2011&batch_title=Selected%20Matches%20for%3A%20Items%20authored%20by%20Komornik%2C%20Vilmos&fmt=doc&pg1=INDI&s1=104490&searchin=&sort=newest&vfpref=html&r=1&mx-pid=3054428
  [5]: https://simonbakermaths.wordpress.com/
  [6]: https://www.researchgate.net/profile/Derong_Kong
  [7]: http://wisdyn.math.uni-bremen.de/betabremen.pdf
  [8]: http://wisdyn.math.uni-bremen.de/Lingmin.pdf