I have become very fond of my set of levels.
In my other work in landscape design and stone works (northstarstoneworks.com), I use levels and transits where needed but let walls meander as the land and design demand.
|an entirely cast base for an oven|
Ultimately, the oven and structure needs to be completed with all edges meeting at common points. The level makes this possible. Your level is also used to keep brick faces aligned. A sturdy two-foot level and a rubber mallet lets you adjust brick faces so that the plane of the oven face, arch face, or throat top are true.
The white stuff around and on top of the oven pictured at the top with me in front is refractory ceramic insulation, essential to keeping the heated mass retain BTU's for days. The chimney, damper, and enclosure details will be addressed in another post.