A quasi-multiplier m on an algebra A is a bilinear mapping from
A
×
A
A \times A
into itself such that
m
(
a
x
,
y
b
)
=
a
m
(
x
,
y
)
b
m(ax,yb) = am(x,y)b
for all
a
,
x
,
y
,
b
∈
A
a,x,y,b \in A
. An introduction to the theory of quasi-multipliers on Banach algebras with minimal approximate identities is given and applications to
C
∗
{C^\ast }
-algebras and group algebras are developed.