Am new in this community,the rapid increase in technology and mathematics related to Bitcoin makes me confuse,am also concerned  about the safety of clients data since all transactions are done on a single public network.
 I brought up this topic because I want more explanation,if there is any development or means outside of the public Blockchain that also stores client data to ensure more privacy. I also learnt about lightweight wallet that connects to full node before any transaction,why is it so.....
Pardon me,if am not expressing my points clearly
 The mathematical expressions is hectic,is there any method or recommendations for me  to begin with so I can assimilate on the Technicals of Bitcoin. And unravel it's possibilities,not for me to be just a Bitcoiner who knows only how to hold and sell but also technically oriented about Bitcoin