Reference for Ergodic Theory I am looking for a good introductory book on ergodic theory. Can someone recommend  some introductory texts on that? 
 A: You could also try
Ergodic theory with a view towards number theory be Einsiedler and Ward.
Direct link to the online edition
The book is available on springerlink. I do have to warn you that the book can be experienced as quite chaotic but the good thing is that the writers are experts on the topic.
A: I recommend Silva, "Invitation to Ergodic theory".  This is a wonderful little book.  He starts from the ground up, assuming no background except for some competence in analysis, and reaches what seem to be important issues in the theory (I am not an expert).  Along the way your knowledge of measure theory should be solidified.  For the total novice, the introduction to measure theory, Lebesgue measurable sets, etc., is the best I've seen.
A: You can try:


*

*Paul Halmos – Introduction to ergodic theory

*Harry Furstenberg - Recurrence in ergodic theory and combinatorial number theory 

*Dynamical systems and ergodic theory – Mark Pollicott, Michiko Yuri.
The last two are developed to be able to prove some combinatorial results such as van der Waerden's theorem and Szemeredi's theorem.
A: You can try with "An Introduction to Ergodic Theory" By Peter Walters, this is a Graduate Text of Mathematics but is really good. Good Luck!
A: Ben Green has made available notes from his Ergodic Theory class here.  They are certainly worth a look.
A: The most basic book on Ergodic theory that I have come across is, 
Introduction to Dynamical Systems, By Brin and Stuck. 
This book is actually used as an undergraduate text, but as a first contact with the subject, this will be perfect. The first few chapters deal with Topological and Symbolic Dynamics. Ch.4 is devoted to Ergodic theory, and is independent on earlier chapters. Subsequenct chapters deal with similar topics. Ergodic theory is notoriously difficult; once you have read through parts of this book, the other books on the subject will not be so intimidating. 
A: Have a look at "Randomness and Recurrence in Dynamical Systems" By Rodney Nillsen. Google books link http://books.google.com/books?id=NkzPSr-JpBwC&printsec=frontcover#v=onepage
A: I know it's not exacly what you are looking for but it's really interesting. As long you start to see some basics definitions and some nice results of finite measure ergodic theory, you should read something about ergodic theory on $\sigma$-finite spaces. The theory is quite different and very beautiful!
Aaronson, J. - An Introduction to Infinite Ergodic Theory. Mathematical Surveys and Monographs, AMS, 1997.
A: The Best Book of ergodic theory, that there, that shows the power of theory in all areas, the book is that of Ricardo Mane:
MAÑÉ, R. - Ergodic Theory and Differentiable Dynamics. Berlin, Springer-Verlag, 1987.
Another book is really interesting: 
Peter Walters - An Introduction to Ergodic Theory.  Graduate Text of Mathematics. Springer-Verlag
The rest of the books are variations of the above two.
A: I like the book Statistical Properties of Deterministic systems by Jiu Ding and Aihui zhong.  
You can read the book online here or can buy it really cheap here Or you can spend way more and buy it on amazon.  
A: Two good books are:

*

*Viana - Foundations of Ergodic Theory;

*Mañé - Ergodic Theory and Differetiable Dynamics

A: Arguably this is not a book but Terence Tao's lecture-blogs (the very first of many as I understand) may be worth looking into: https://terrytao.wordpress.com/category/teaching/254a-ergodic-theory/ .
Rudolph's Fundamentals of measurable dynamics. Ergodic theory on Lebesgue spaces is also noteworthy in my humble opinion.
