  The purpose of this paper is to study Lie-Rinehart superalgebras over
characteristic zero fields, which are consisting of a supercommutative
associative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in
a certain way. We discuss their structure and provide a classification in small
dimensions. We describe all possible pairs defining a Lie-Rinehart superalgebra
for $\dim(A)\leq 2$ and $\dim(L)\leq 4$. Moreover, we construct a cohomology
complex and develop a theory of formal deformations based on formal power
series and this cohomology.
