How dinosaurs evolved into birds and mammals?

Mammals did not evolve from dinosaurs.

Birds branched off from a group of dinosaurs called theropods, the two-legged carnivores that included T. rex and Velociraptor. Even before birds evolved many theropods already had feathers, probably for insulation. From here there are two main hypotheses about how these dinosaurs evolved into birds.

First is the "ground up" hypothesis, which proposes that small theropod dinosaurs held their arms out in chasing prey such as insects. Certain arrangements of feathers might have allowed them to run faster or lighter, which became enhanced as the arms became precursors to wings. This then gradually transitioned into "wing" aided jumping, then gliding, and finally true flight.

Second is the "trees down" hypothesis. It proposes that small, tree-climbing theropods that jumped from branch to branch were able to use their feathers on their arms and legs for gliding, this gradually developed into true flight. Fossils that may match this description have been found.