As a Private Pilot, you will need to master following:

• air traffic control operations
• air transport law
• aircraft flight control systems
• apply airport standards and regulations
• apply signalling control procedures
• aviation meteorology
• civil aviation regulations
• common aviation safety regulations
• communicate in air traffic services
• comply with air traffic control operations
• ensure compliance with civil aviation regulations
• follow airport safety procedures
• implement airside safety procedures
• operate two-way radio systems
• perform flight manoeuvres
• perform routine flight operations checks
• perform take off and landing
• pre-flight procedures for IFR flights

More generally, a private pilot is also versed in:

• ensure ongoing compliance with regulations
• geographic areas
• have spatial awareness
• identify airport safety hazards
• operate cockpit control panels
• operate radar equipment
• operate radio equipment
• operate radio navigation instruments
• perform risk analysis
• read 3D displays
• read maps
• undertake procedures to meet aircraft flight requirements
• use different communication channels
• visual flight rules

It also helps to know the following:

• use meteorological information
• work in an aviation team
• make independent operating decisions