Learning system software could mean the tools that support teaching such as learning management systems (LMS). There are not many books about research on those tools. The term could also mean analytics tools. There are a number of books related to learning analytics, including one from Information Age Press I have a few chapters in.

Packiya Raj -

The book edited by Yefim Kates, titled, "Learning Management Systems and Instructional Design: Best Practices in Online Education" 1st Edition, may be useful.

if you mean Learning Management System by Learning system, then, there are plenty of them. Some liked Moodle is even free. There are low costs systems such as Learning Dash that works with Wordpress. All of them come with elaborate online documentation and tutorials.