There is nothing like core HR.
Please be informed that HR has different functions and its not possible to learn everything at once. Exactly why all the good positions in HR requests atleast 2 years of experience.
Also be informed that HR is a daily learning process, you will come across issues that are unique each and every day.
Anyways if what you are looking at is a Generalist profile its a gradual process:
The role includes
Compensation & Benefits
Pay slip Distribution
Time sheet Management
Employee Information/ Skill Management
Exit Interviews & Process
Health & Safety
Though nowadays in major companies the roles have been revised in the following manner:
Also please have a look at the attached document for more details.