Ubuntu phone in 2019
Solution 1:
Ubuntu Edge was a project that failed to meet crowdfunding requirements. You can find the whole story on Wikipedia
Canonical has stopped its official support to Ubuntu Touch (the OS dedicated to phones) in 2017. The code is now maintained by the UBports community. As far as I know it is not possible to buy an Ubuntu phone, if you wish to install it you'll have to purchase a phone and make the installation yourself. Some phones are supported by UBports. I never gave a try myself as the maintained phone are difficult to find or over expensive in my opinion. But the UBports community is alive and delivers regular updates.
Some projects of open source phones are normally coming, such as Purism Librem 5, PinePhone or Necuno. I follow them regularly as I hope it will be possible one day to install Ubuntu Touch on one of them.
2020 update
The PinePhone project has progressed recently. It is now possible to pre-order a PinePhone with UBports installed :) You can have a look into Pine64 Store to know a bit more about it and decide if you want to give it a try.