#On to what does the author of Hebrews want the believers to press?

The author of Hebrews wants the believers to press on to maturity. [6:1]

#What teachings does the author list as the foundation of the message of Christ?

The foundational teachings are repentance from dead works, faith in God, baptisms, laying on of hands, the resurrection of the dead, and eternal judgment. [6:1-2]