Nashor's Tooth is a must because of the CDR, AS, and AP damage on basic attacks. Because Varus is usually played as an ADC his cooldowns are never as short as I would like them to be so it is important to max CDR on him as early as possible. AP Varus relies on getting three stacks of Blighted Quiver on his opponent quickly so he can follow up with an activating ability, making AS very important. One of the best things about AP Varus is that he is a mid who can do pretty high damage with his auto attacks which gives him something to do in team fights when his abilities are on cooldown. It also make farming really easy throughout the game.

Zhonya's Hourglass is really good simply because it gives high AP and an awesome active which can save an AP Varus whose abilities are still on cooldown.

Runaan's Hurricane is what gives Varus what I would consider "Rediculus late game AOE damage." Imagine a team fight next to Baron Nashor in which Varus (who has 400 AP) gets nine auto attacks off (that wouldn't take very long). After the first three autos (~600 mixed damage - resistances{half damage for Runaan's bolts}) he cast his Hail of Arrows which does 205 + Blighted Quiver which does 39% of target's (at most three targets if you land a good e) maximum health!!!! (minus resistances) You get three more autos off and activate them with you ult or q to blow up your next victim. Anyway you get the point. Buy Runaan's :)

AP Varus gets his high damage from his w...max it first. If you are playing against a high ranged mid and want more poke max q second otherwise I go for his e which gives him easy aoe activation for w stacks (works great with Runaan's Hurricane)

If you are playing against an AD mid then you absolutely need the armor seals (same for mr blues if playing against an AP mid), but if you are playing against a melee champ (AP or AD) I would recommend going full AP/Magic Pen. This aggression is made possible because of Varus' high cc kit and his ability to harass and kite most melee champions.

Pretty standard for offensive AP Mid. I chose to go with max CDR for flash/ignite/zhonya's just because he has terrible mobility and in that little bit of time a flash could be necessary.

PROS

• easy to farm with
• high late-game damage
• great aoe damage (with Runaan's Huricane)
• two great cc abilities (three with Rylai's Crystal Scepter)
• easy to manage mana
• people are not expecting this build...surprise them!

CONS

• very farm/item dependent
• cannot build defensive otherwise you become pretty useless
• requires good positioning because of Varus' lack of mobility