  A generalized notion of a Lie algebroid is presented. Using this, the Lie
algebroid generalized tangent bundle is obtained. A new point of view over
(linear) connections theory on a fiber bundle is presented. These connections
are characterized by o horizontal distribution of the Lie algebroid generalized
tangent bundle. Some basic properties of these generalized connections are
investigated. Special attention to the class of linear connections is paid. The
recently studied Lie algebroids connections can be recovered as special cases
within this more general framework. In particular, all results are similar with
the classical results. Formulas of Ricci and Bianchi type and linear
connections of Levi-Civita type are presented.
