William Dunham lectures at Cornell on two of Euler’s big theorems: the divergence of the sum of the reciprocals of the primes and the evaluation of the sum of the reciprocals of the squares
Dunham is the author of Euler: The Master of Us All, which focuses on selected results of Euler. If I recall correctly I first saw the evaluation of 
This focuses on the math; there’s a full-length biography of Euler coming out, by Ronald Calinger. The publisher, Princeton, describes this as the “first full-scale biography of Leonhard Euler”, which is honestly a bit surprising.
God plays dice 
“Euler: The Master of us all” is a fantastic book, I can not praise it highly enough. The maths is made easy enough to follow (as a science graduate), yet not trivially so. Since it covered a lot of Euler’s proofs I was unfamiliar with, pulling together mathematical techniques I was familiar with, it was incredibly enlightening and rewarding to read. The quality of writing is outstanding, aside from the details of maths you get a picture of what was going on at the time, and interesting biographical detals of Euler. I quite often take it on holiday with me and reread chapters. Sad, I know.
Prior to reading the book I had obviously come across Euler, however I had not realised how much he had contributed, nor that he had continued undeterred after going blind. What an amazing person, really an all time giant.