Hey there, fellow summoners! Welcome to my Olaf solo top build.
The idea of this build is to be tanky and be able to deal tons of damage.
Olaf is a great champ and lots of fun to play.

Read on for my explanation for the chosen items, skills and spells in my build.

The start of the build is a basic Boots + 3x Health Potion
From there I chose double Doran's Blade which will provide you with early game Dominance. They offer some life steal, AD and HP, which is perfect for .
Phage is going to help greatly by giving you more HP and some AD as well as building towards a Frozen Mallet .
Mercury's Treads should be bought after Phage - but can be substituted for Ninja Tabi if you are fighting an AD champ, or for whatever reason.
Warmog's Armor is good to get fairly early as Olaf's E is where he does the damage and it costs health to use it. When you get an Atma's Impaler , Frozen Mallet and Warmog's Armor will be even more useful (because of Atma's Impaler's passive).
Maw of Malmortius is a good late game item but it isn't that important. The extra AD and Magic resist will be very helpful though.

Last is Guardian Angel . As with most builds, this is just an extra but its still a useful item. If you'd rather choose something else, I'd recommend Sunfire Aegis or Madred's Bloodrazor .

Olaf's main damage dealer is his E. It deals true damage and costs a portion of his health. The cooldown is very quick and it can be used several times during a fight because of this.
I always pick his Q first. This is because it is a good poking ability and the cooldown is almost entirely refreshed if you pick his axe up. This is an awesome move to have when chasing somebody as it also slows the enemy and you may pick you axe back up whilst following them (which could result in several slows in concession).
His W is still good but I get it 4th and max it last because I feel that his other abilities are better early-mid game (for poking and lots of damage). His W is still great for fights and taking down turrets etc.

Ghost is great for escaping when used in conjunction with his ulti (which removes all stuns, slows etc.). I have run away from a 4-5 man gank with this combo and lived.
Ignite is for obvious reasons and gives you that offensive edge in fights.

This build is very strong and when used right, could definitely rake up the kills.
Let me know, in the comments, how well you did with this build and what you think of it.

You can expect more guides (an Olaf jungle guide is quite likely) to come!

Any suggestions for edits are welcome and I love feedback - good or bad.

Good luck on the Fields of justice!