Phosphoglucomutase - catalyzes the interconversion of glucose-1-phosphate (G1P) and glucose-6-phosphate (G6P).
This enzyme is the common link between glycogen
biosynthesis and glycogen breakdown.
UDP-glucose pyrophosphorylase - catalyzes the transfer of glucose (from G1P) to uridine triphosphate, forming UDP-glucose and pyrophosphate.
G1P + UTP <=> UDP-Glucose + PPi
This has the effect of "activating"
glucose for incorporation into the growing glycogen chain in
the next step of the process. Furthermore, this reaction is made
essentially irreversible by hydrolysis of the pyrophosphate to
2Pi.
Glycogen Synthase - catalyzes the formation of an 
(1->4) glycosidic
bond between carbon 4 of an existing glycogen chain and carbon
1 of a glucose (from UDP-glucose). UDP is released in the process.
Glycogen synthase is the major point of regulation of glycogen
biosynthesis. The reaction is depicted in Figure
16.9.
Amylo-(1,4->1,6)-transglycosylase
(branching enzyme) - This enzyme,
most commonly called branching enzyme, introduces the
abundant (1->6) branches, which are characteristic
of glycogen molecules. The reaction transfers a terminal fragment,
some 6 or 7 residues long, from a branch terminus at least 11
residues in length to a hydroxyl group at the 6-position of a
glucose residue in the interior of the polymer (Figure
16.10). As a result of the transfer, two termini recognized
by glycogen synthase are created where only one existed before.
This means that the synthesis and the mobilization of glycogen
can proced quickly and efficiently, depending on the needs of
the cell.