Overlapping phases and age norms
It is important to keep in mind that infant motor development does not occur as a progression of stages with standardized age norms, but rather as a cascade of emerging abilities, with each new ability building on acquired abilities. These phases overlap with individual infants having their own timetable for acquiring new abilities.
From birth infants pay attention to their hands and soon after start to move their hands in the direction of toys within reach.
At 5 weeks Will has developed more control of his upper and lower extremity actions and his ability to stabilize the head and trunk to support these actions has improved.
Reaching, batting and early exploration of interesting objects
At 9 weeks Will's hand actions are starting to reflect 
At 15 weeks (third month) Will displays the full range of hand and finger actions, as well as exploratory, grasp, transport and manipulation abilities typically 
Using the hands to grasp, manipulate and inspect toys 
Reaching for, grasping and manipulation become more accurate and focussed. 
In this tutorial you see Will (5 months 3 weeks) playing with a two 2 plastic links and a rattle.
Shaking, inspecting, banging, passing from hand-to-hand