Once you get your hands on the hookblade in Sequence 2, it’ll quickly become a valuable part of Ezio’s kit for getting around the city and committing various acts of mischief.
Firstly, the hookblade allows you to perform a few acrobatic techniques. You can extend your reach automatically when jumping upwards as you climb to reach hard-to-get-to ledges. Also, pressing the Circle/B button when in mid air and about to grab onto a turn-lantern or other hanging object will propel you forwards instead at great speed.
In combat, the hookblade has a few interesting uses. It can be used for a hook-and-throw counter (which instantly and non-lethally takes an enemy out of the fight), or even a hook-and-steal, which allows you to pickpocket an enemy in the heat of battle.
It has a few uses when it comes to avoiding and escaping the enemy, too. You can perform a hook-and-run to flip over your enemy and keep moving, allowing you to get through the cordons of enemies that block your progress. You can also tap the button again mid-animiation to throw them to the ground instead - particularily humourous when used on lone rooftop guards to toss them into the street.
Finally, the hookblade can be used to collapse the scaffolding structures around the city to throw off pursurers, or even take out a few. It’s an easy way to get a Trophy/Achievement too with the creative use of some Caltrops.