  We present a development of the theory of higher groups, including infinity
groups and connective spectra, in homotopy type theory. An infinity group is
simply the loops in a pointed, connected type, where the group structure comes
from the structure inherent in the identity types of Martin-L\"of type theory.
We investigate ordinary groups from this viewpoint, as well as higher
dimensional groups and groups that can be delooped more than once. A major
result is the stabilization theorem, which states that if an $n$-type can be
delooped $n+2$ times, then it is an infinite loop type. Most of the results
have been formalized in the Lean proof assistant.
