Can you steal something when someone isn't looking in Skyrim?

I will admit, I have 3 save files in Skyrim and play it all the time, but I have completely avoided stealing items. I'm currently contemplating on whether or not I should steal a book from the Battle-Borns. The only current inhabitant of the house is Lars, a child. Idolf, the only adult, left. Can I steal the book I need without Lars or Idolf or any of the guards knowing?

Yes.

If you are completely hidden (use the stealth indicator when sneaking to check) when you take the book, you won't be noticed. NPCs only see items vanish if they are looking when you take them- they won't (except in certain scripted events) notice the item is gone just by looking at where it was.

Yes, if you crouch and are shown to be hidden you will be able to steal the item in question with out being caught. It is only Pick-Pocketing that has a chance to alert someone if you fail. When the item is just in the environment you always succeed.

However. The game has a secondary tracking system you should be aware of. It does not matter how much you take and if no one sees you there is always a random chance that the person you took an item from will hire thugs to come and 'teach you a lesson'. This is outside of the law and defending yourself from them does not count as an attack or murder if witnessed. But it is something to be aware of that can happen.

The main way to steal in Skyrim is to actually do it while their not looking. An easy guide to stealing:

1. Make sure their not looking, OR, this indicator:

   

   Which should look like -.- meaning that your hidden.

2. Use your action button (PC: E, PS3: X, 360: A) when it gives the notification to do so. (In this case, it is Brynjolf (SPOILER) we will be stealing from.

3. After the menu pops up, you get a chance to successfully take items as shown below:

   

   As shown above, you get the items description, and the chance to steal. Depending on the amount of items your stealing and the value, it can range from 100% to 0% so be careful to save if you don't want to have the chance of getting caught.

4. Take the items, back out and walk away like it never happened.

   Just remember: This is Skyrim, not real life, it's not a crime to stick your hand in someones pocket and search through all their belongings, the second you pull it out, it is one.

More information about Stealing can be found on the wiki.

Good luck and don't get caught.