Itunes impossible to download

Have you tried a different browser on your Mac/PC, and/or tried clearing the history and cache on the browser that you are using ? If you have popups blocked then that might also prevent it from downloading.

If you are trying to do it on your phone then you can't, you can only update the built-in apps by updating the phone's iOS version - if your phone is on 7.0.4 then its built-in apps are up-to-date

If you have iTunes already installed on your computer then can you download it via, if using a Mac, iTunes > Check For Updates, or if using a PC 'Help > Check For Updates' ? Or have you got a second browser installed on your computer that you could try ?