Building a brick oven requires determination and perseverance, with the help of a few tools!
Here's a list of the tools and materials I used during the build

Power tools

wet brick saw: to cut firebricks
angle grinder: to cut firebricks and stones
cement mixer (not indispensable as you can mix by hand in a wheelbarrow)
hand cement mixer (same as above)
jigsaw (to cut templates for the different arches)
circular saw: to cut wood planks for concrete forms (optional, you can use hand saw)
power drill: to drill holes for rebars

Other tools

ruler/measuring tape: to measure what should be measured
try square: to make sure what should be square is indeed square
spirit level: to make sure what should be horizontal is indeed horizontal
masonry trowels: for brick laying. I used a smaller one to finish the joints
hoe/shovel: to mix the perlite and cement
sponge: to clean the cement residues on stone
water spray: to wet the bricks
steel brush: to clean mortar joints between stones (not for bricks)
gloves: for mortar which is alkaline. I used a few pairs during the project
stone chisel + hammer: for stone work
wheelbarrow: mostly used to mix the perlite and cement since you normally don't use a mixer as it would deteriorate the perlite.
protection mask: used when mixing cement, perlite, and while cutting firebricks and stones
ear plugs: wet saw and angle grinders are your ears enemies! (also useful to insulate yourself from unsolicited advice)
protection glasses: when cutting with grinder/wet saw/chisel
pencils
calculator

Software

This is totally optional, but if you already know a 3d software or are willing to learn, it will help you to plan your oven. Of course pencil and paper are still valid, and I believe that's what our ancestors used since they didn't have electricity to power their computer to run the above mentioned 3d software.

The advantages of a 3d model are numerous:

plan your dome: tune the dimensions, get an estimate of firebricks usage
model the enclosure and adapt it so it fits with the surroundings
easily plan where you want that oven to be: the nice thing with a 3d model is that once you design it, you can move it where you want, so if you have a lot of space, you could even model it and choose the optimal place you want it to be (provided your create a model of your garden/courtyard).
In my case I only had one possible spot, but I nevertheless modeled the surrounding walls which are basically just some planar surfaces textured with real photographs of the existing walls. This way you have the closest image of what it will eventually look like.
This also helps to decide whether you actually want an oven in your garden!

I personally used Maya, but there are many others possibilities (Blender, Sketchup ...).

Believe me, it's really useful!

Materials

Here's a list of materials I used

Foundation + hearth

stones, reinforced concrete (8mm rebars + fibers)

Hearth insulation

perlite (~ 3-5mm granularity) + Portland

Cooking floor

refractory bricks (22x11x6)

Oven dome

refractory bricks + refractory mortar (1 Portland, 3 sand, 1 lime, 1 fire clay)

Dome insulation inner layer

perlite + air entrained cement

Dome insulation outer layers

rockwool panels ( 0.039 W/mK)

220 refractory bricks, 600 kg in a Berlingo

Bricks waiting to be assembled

The wet saw with diamond blade I used. It only had a 65mm cutting depth.