package
{
    import flash.display.MovieClip;
    import flash.events.KeyboardEvent;
    import flash.events.Event;

    public class Hero extends MovieClip
    {
        var leftKeyDown:Boolean = false;
        var upKeyDown:Boolean = false;
        var rightKeyDown:Boolean = false;
        var downKeyDown:Boolean = false;
        var mainSpeed:Number = 7;
        var mainJumping:Boolean = false;
        var jumpSpeedLimit:int = 15;
        var jumpSpeed:Number = jumpSpeedLimit;

        public function Hero()
        {
            addEventListener(Event.ENTER_FRAME, moveChar);
            stage.addEventListener(KeyboardEvent.KEY_DOWN, checkKeysDown);
            stage.addEventListener(KeyboardEvent.KEY_UP, checkKeysUp);
        }
        public function moveChar(event:Event):void
        {
            if (leftKeyDown)
            {
                Hero.x -=  mainSpeed;
            }
            if (rightKeyDown)
            {
                Hero.x +=  mainSpeed;
            }
            if (upKeyDown || mainJumping)
            {
                mainJump();
            }
        }
        public function checkKeysDown(event:KeyboardEvent):void
        {
            if (event.keyCode == 37 || event.keyCode == 65)
            {
                leftKeyDown = true;
            }
            if (event.keyCode == 38 || event.keyCode == 87)
            {
                upKeyDown = true;
            }
            if (event.keyCode == 39 || event.keyCode == 68)
            {
                rightKeyDown = true;
            }
            if (event.keyCode == 40 || event.keyCode == 83)
            {
                downKeyDown = true;
            }
        }
        public function checkKeysUp(event:KeyboardEvent):void
        {
            if (event.keyCode == 37 || event.keyCode == 65)
            {
                leftKeyDown = false;
            }
            if (event.keyCode == 38 || event.keyCode == 87)
            {
                upKeyDown = false;
            }
            if (event.keyCode == 39 || event.keyCode == 68)
            {
                rightKeyDown = false;
            }
            if (event.keyCode == 40 || event.keyCode == 83)
            {
                downKeyDown = false;
            }
        }
        public function mainJump():void
        {
            if (! mainJumping)
            {
                mainJumping = true;
                jumpSpeed = jumpSpeedLimit * -1;
                Hero.y +=  jumpSpeed;
            }
            else
            {
                if (jumpSpeed < 0)
                {
                    jumpSpeed *=  1 - jumpSpeedLimit / 75;
                    if (jumpSpeed > -jumpSpeedLimit/ 5)
                    {
                        jumpSpeed *=  -1;
                    }
                }
                if (jumpSpeed > 0 && jumpSpeed <= jumpSpeedLimit)
                {
                    jumpSpeed *=  1 + jumpSpeedLimit / 50;
                }
                Hero.y +=  jumpSpeed;
                if (Hero.y >= stage.stageHeight - Hero.height)
                {
                    mainJumping = false;
                    Hero.y = stage.stageHeight - Hero.height;
                }
            }
        }
    }
}

And this is the error I keep getting on like 20 lines:

\\Hero.as, Line 28 1119: Access of possibly undefined property height through a reference with static type Class.

How can I resolve this?

Do you get the same error in every line? However, the error might be that with "Hero" in lines like "Hero.x +=  mainSpeed" you're targeting the class, while you should target the instance. So try replacing all the "Hero"s with "this", except for the class name and the constructor function.

I got your point, I made a new MovieClip and named it mainChar, changed the Hero to mainChar in my script and renamed the script to: Character. I get this error on like 30 lines: \\Character.as, Line 20 1120: Access of undefined property mainChar

Try using the keyword "this", it targets automatically the instance the code is running for.

Gabo thanks for your help, I finaly got the script working, please lock this thread.