I have made this page to track the battle between YPG / Peshmerga and Da’esh. The images are from the Wikipedia page for ISIL. To view the progress of the battle, click on any of the images and use the arrow keys in the gallery. The thumbnails below only show part of the map.
The battle is still within the city.
The battle is still within the city.
The battle is still within the city.
The battle is still within the city.
The battle is still within the city.
The city was liberated on the 26th January 2015
Kurdish forces break out.
The rest is pretty self-explanatory ->
On the night of 21 -22 February the Turkish Army evacuated the Tomb of Salesman Shah. (Qarah on the map.)
Battle of Sarrin
Sarin still surrounded. Kobanî Kurds advance East. Note also advances further east.
Rojavan forces surging towards Tall Abyad in the East.
Closing in on Tal Abyad
Tal Abyad liberated
Da’esh launches a terrorist attack on Kobani. There are accusations and denials of Turkish complicity.
Interestingly, the Turkish excursion to rescue the Tomb of Suleyman Shah on 21 February was almost entirely through Kurdish-held territory. One wonders if they weren’t really rescuing it from the Kurds. They didn’t do much when Da’esh surrounded it. 
Damage to Kobanî as at mid-February 2015 (BBC)
So far the Kurdish fighters appear to have largely confined themselves to areas inhabited by Kurds.
Michael Cope's Blog 