Simple Rectangle Collision Detection

We use collision detection all the time. Grabbing a cup of coffee, scratching our nose, sitting on a chair... even when walking our body detects the presence of other objects and surfaces outside of its own.
For computers it's a bit different. They can't detect anything unless we tell them how.

(Unrotated) rectangle collision is one of the simplest ones. If any point (P) isn't between the coordinates of both axis of the rectangle (R), then it's not colliding:

if ( P_x >= R1_x  AND  P_x <= R2_x  AND
     P_y >= R1_y  AND  P_y <= R2_y){

     // The point is inside the rectangle
}
else{
     // The point is outside the rectangle
}

With 2 rectangles (R1 and R2) we need to check, on both axis, if the coordinates of the edges of the 1st rectangle is between the coordinates of the 2nd:

if ( R1_x2 > R2_x1 AND R1_x1 < R2_x2 AND
     R1_y2 > R2_y1 AND R1_y1 < R2_y2 ){

     // The rectangles collided
}