I am simply here to teach you one of the best mid lane champions in LoL. Anivia has been my favorite champ and even though the changes in 6.9 did her dirty, it does not affect her much (but thank god they are buffing the range on her ult.) With this guide you will learn how powerful this bird still is.

Pros:
Insane Late Game
Strong Utility
OP Passive
Can Push Lane Well w/Ult
Diverse Build Paths
Still OK if Behind
Strong TP Ganks
Unique Play Style
Cons:
Mana Hungry
Tough Laning Phase
Hard to Learn All Combos
Needs Good Positioning
Unique Play Style

Unique play style is both because I really enjoy champions with unique play-styles. It is a con because you cannot translate skills from another champion to her.

Before the Game
Adjust Masteries, Runes, Sums depending on lane matchup. Take TP if not looking/cannot acheive kill in lane. Anivia has good TP ganks due to tons of CC, damage, and her wall.
Laning Phase
Laning Phase can be tough for many reasons. The most simple one is her AA animation is pretty bad to CS with. They buffed it a bit in 6.9 to be average. Also, Blackfrost Anivia's AA animation is a huge improvement over classic skin. Anivia has some tough lane matchups but just focus on farming. You can use Q-E to punish enemy for farming if you are good at the combo. Post 6 ult is great for waveclear. I normally base, push wave, look for gank (whether TP gank or not.) Anivia excells in Team fights. Especially early with passive because the enemy will not be able to kill you without taking casualties themselves. Finally, ASK FOR BLUE BUFF. Helps a TON early game.
TeamFight/Late Game
Anivia has really good objective control and 2 AOE abilities. These are 2 crucial components of late game. Her AOE in teamfights and CC is unmatched. Just sit back and throw abilities with your huge mana pool. At this point R-E is your main combo.

I LOVED RoA pre-6.9 mainly for Catalyst Passive. Great instant Regen. The raw stats were great but you would not get them until Rod was fully stacked at about 25 min. I would normally go this without tear and have fine mana sustain. 6.9 changed that. Tear is alot better on her and the new catalyst passive is bad. BAD. The only way to regen mana is to take damage. Anivia is INSANELY squishy early game and I do not want to take damage EVER with her. This new passive, along with RoA I believe should be only built on Fighter/Mages that are near the front lines like Swain and Ryze. I like Hextech for similar but instant stats and the active. The active is really good if someone gets to close to you or to chase them.
Tear is better because of the refund, then Lost Chapter for the great passive, then finally the catalyst for some tankiness and mana.