  All known Moufang sets arise, in some way or another, from an algebraic
structure which can be called `division' in some way. In this PhD dissertation,
I made an attempt to develop a theory of local Moufang sets, which generalize
Moufang sets in a way to allow constructing using the corresponding local
algebraic structures. In the first of the two major parts of the dissertation,
I develop the theory of local Moufang sets, while in the second part, some
examples are constructed. The most general example constructed arises from a
local Jordan pair (which corresponds to a local Jordan algebra), and one of the
main theorems characterizes these local Moufang sets.
