this is a reference request question.
I have recently developed interest in operator algebras and it has come to my attention that there is plenty of ongoing research at the intersection of that field with ergodic theory and group actions. I would like to have a good look at all that, however, I have only elementary knowledge of group theory and zero knowledge of ergodic theory and dynamical systems in general.
Could anyone help me develop a "study path" towards that area?
On
I an amateur in ergodic theory myself, but I found the popular introductory text Ergodic Theory With a View Towards Number Theory to be an excellent text. It's relevant for you since chapter 8 introduces actions of groups on dynamical systems, and the book specifies a minimal path for you to get to that point, chapters 2, 4 and 8 to be precise.
As far as I know, there is no textbook on this subject. You have to mix and match different sources. All books written on the subject are geared towards proving a particular "big" theorem (or several "big" theorems).
I would start with
'Introduction to Dynamical Systems', by Brin and Stuck.
It is written as a textbook but this book hardly deals with group-theoretic aspects of the ergodic theory.
Then proceed to
'Ratner’s Theorems on Unipotent Flows', by Morris-Witte,
more specifically, chapters 1-4 which can serve as an introduction to group-theoretic aspects.
If you manage with these, either read chapter 5 or switch to
'Ergodic Theory and Semisimple Groups', by Zimmer,
more specifically, chapters 1-4.
As an alternative to all of the above, take a look at the volume
'Ergodic theory, symbolic dynamics, and hyperbolic spaces',
specifically, chapters 1, 2, 3, 4, 9.
This book also can serve as an introduction to the subject (with a different emphasis, of course).
However, I strongly suggest you to talk to your graduate advisor, since reading these sources can seriously distract you from working on your thesis (I assume, you are a grad student).