SRE is a specialized software engineering discipline, the sort of thing you'd do if you had a team of 20 SWEs and wanted to write something like Kubernetes or Puppet. Good books on SRE (besides the Google book that popularized it) cover UNIX and Linux operating system concepts, low-level networking, and software architecture in general.
On the other hand, if you've got a team that does a lot of operations work by hand -- runbooks, MOPs, checklists, etc -- and want to automate it, then you should be looking for books on modern systems administration. Look for references to specific technologies such as Kubernetes (or Mesos), Terraform (or CloudFormation, or Pulumi), Puppet (or Ansible).
(context: I've been an SRE for ~10 years, first at Google then Stripe)