It's less formal than 'regarding' but more formal than 'about'; suitable for professional and academic contexts. Please see the detailed report in regard to the project's progress.
Pro Tip 2/3
Connecting Ideas
Use it to connect what you’re talking about to your main topic, linking ideas smoothly. In regard to your question, I will need more time to provide a thorough answer.
Pro Tip 3/3
Transitions in Speech
It's often used to smoothly transition to a new point in presentations or discussions. With regard to our sales targets, we need to increase our efforts.