Book recommendation for ergodic theory and/or topological dynamics?

For me the standard text is Peter Walters, "An Introduction to Ergodic Theory", Springer Graduate Texts in Mathematics.

I think another good choice is the book "Ergodic Theory: With a View Towards Number Theory" by Manfred Einsiedler and Thomas Ward,Graduate Texts in Mathematics 259.Besides basic concepts of ergodic theory,the book also discusses the connection between ergodic theory and number theory,which is a hot topic recently.And a forthcoming second volume will discuss about entropy,drafts of the book can be found on the homepage of Thomas Ward (https://tbward0.wixsite.com/books).

I really like (and recommend) Billingsley's Ergodic Theory and Information. It is a well-written book with very clear explanations. For example, his treatment of entropy tops those in both Walter's An Introduction to Ergodic Theory and Petersen's Ergodic Theory, both of which are also good books though.