Is muon muon annihilation already realised? As muon colliders do not yet exist, has muon-muon annihilation already been realized experimentally?
 A: The direct annihilation of a muon with an antimuon wouldn't be distinguishable from other processes in a collision between high-energy beams. A collider would generate a whole menagerie of complicated processes, much like the Large Electron-Positron Collider did before its tunnel was repurposed by the LHC.
However, if the muon and antimuon first undergo an electromagnetic capture reaction and form true muonium, then annihilation (a QED process) becomes much more likely than the weak decay of either muon.
My initial instinct was that production of true muonium would require cooled ensembles of muons and antimuons to interact with each other, as is done to produce muonic hydrogen or the electron-muon bound state (which is, confusingly, also known as muonium). However, Wikipedia links to a 2019 paper predicting that true muonium should discoverable using the LHC Run 3 data set, which will be collected in the next three or four years.
A: A muon and an anti muon can annihilate but not a muon and a muon. They are not antiparticles. Two muons could exchange energy and momentum between each other though. 
Muon antimuon annihilations works like this where the muons annihilate into a Z boson and this Z boson decays to electron neutrino and an antielectron neutrino.
$\mathrm\mu^-+\mu^+=Z^0$
$\mathrm\ Z^0=\nu_e+\bar{v_e} $
