How do networks of strategic agents form and what is their ultimate topology? No engineering literature addresses this question correctly or systematically. Existing economics literature that addresses these questions assumes complete information: agents know in advance the value of linking to other agents, even with agents they have never met and with whom they have had no previous (direct/indirect) interaction!! This paper addresses the same questions under what seems to us to be the much more natural assumption of incomplete information: agents do not know in advance, but must learn, the value of linking to agents they have never met. We show that the assumption of incomplete information has profound implications for the network formation process and the topologies that ultimately form.