  In this paper, the definitions of algebras of quotients and Martandale-like
qoutients of Leibniz algebras are introduced and the interactions between the
two quotients are determined. Firstly, some important properties which not only
hold for a Leibniz algebras but also can been lifted to its algebras of
quotients are investigated. Secondly, for any semiprime Leibniz algebra, its
maximal algebra of quotients is constucted and a Passman-like characterization
of the maximal algebra is described. Thirdly, the relationship between a
Leibniz algebra and the associative algebra which is generated by left and
right multiplication operators of the corresponding Leibniz algebras of
quotients are examined. Finally, the definition of dense extensions and some
vital properties about Leibnia algebras via dense extensions are introduced.
