If you're thinking of picking up Little Witch Academia: Chamber of Time, be aware that it doesn't have an autosave feature.
I found that out the hard way after quitting to the main menu after the first 45 minutes or so of play. Your first opportunity to save in Little Witch Academia: Chamber of Time will be after about an hour's worth of play. Basically once the game has truly begun.
You'll first be able to save your game in the secret chamber accessible from the library. Lotte will bring your attention to a crystal ball on the floor, and being the good friend that she is, will give you a magic potion so that you can spring it into life. You'll need to press the square button to bring up the spell menu, select telepathy magic, and then cast it on the crystal ball. From then on, you can save your game by interacting with it.
You can save your game at any crystal ball dotted around Luna Nova Academy, but first you must activate them. Acquire some telepathy magic potions from the academy store as soon as possible, and make sure you activate the crystal ball in your room. Not far into the game you even gain the ability to fast travel between live crystal balls. You'll need potions to do that too though.
Get into the habit of activating crystal balls as you discover them, and save your game frequently. It's easy to forget that the game doesn't autosave, and you really don't want to lose any progress. You'll quickly lose interest in the game if you keep having to repeat yourself!