Chapters are following.
Just for information: this is my first Guide, i'm at this time lvl 17 and this Guide was written at 03:43am.
So if there are any mistakes or you could improve something, please be kindly and help me a bit.

I think, I'll add the chapters tomorrow if i have enough time.

In my Opinion, starting with Doran's Ring is the smartest way to begin the game. It's not necessary, because you'll sell this item in the late-game anyway, so you can also start with Mana / Heal - Pots, if thats easier for you.

As second item i recommend the Sapphire Crystal, or Catalyst the Protector instant, because you'll use our spells very often, so you'll ran out of Mana pretty fast.

After that you can start buying your Boots. I think, they are not so important, because you can slow and stun to catch your enemy. But the Tenacity and Magic Resist of Mercury's Treats are very useful, little helpers.

As you finish your boots it is highly recommended that you get the Rod of Ages as soon as possible, because he will push your AP (which is also mostly your Damage) AND Health over the amount of most of your Enemys.

After this, it is mostly your decision, which item you buy next. I prefer buying Nashor's Tooth, because he reduces your cooldowns for 25%, followed by Rabadon's Deathcap because this will push your AP as much as possible (140AP + 35% of your AP (so even if you haven't any AP before, after this you would have 189AP....)).