Most of these beginner tutorials were made for Principia 1.4. While they are still up-to-date, the screenshots may not precisely reflect the current game. Updated screenshots are coming within due time.
Building a Vehicle Part 1: CT Mini for Forward and Reverse
Building a Vehicle Part 2: Adding brakes using a Linear Motor
Building a Vehicle Part 3: Angled Cannon using the Servo Motor
Adventure Contraptions Part 1: Doors and traps
Adventure Contraptions Part 2: Elevators, moving platforms, laser puzzle and more