I am considering leaving my current job before my first year contract ends. My contract states that I must give 2 month's notice before leaving. Will I be liable for damages/compensation, etc. if I give them just 1 month's notice?
Once you made up your mind and your employer understands that you are not interested in continuing work, most will let you go asap unless they're short handed and need you to train someone who will take over your job. But given that you're in first your first year that's unlikely.
Anyway I generally recommend to leave your job after having secured your next gig. You don't want to end up being jobless for months with little experience.