TITLE: Good lecture notes/books on Jacobian of hyperelliptic curve
QUESTION [7 upvotes]: I want to understand what the Jacobian variety is from an algebraic (or arithmetic?) perspective.
I want to know:

What is the definition of the Jacobian?
Widely know facts about it.
Why the Jacobian of an elliptic curve is the curve itself.
How to map points on a hyperelliptic curve to the Jacobian.
As much as possible about the torsion subgroup and torsion 2-subgroup of the Jacobian of a hyperelliptic curve
What is the connection between the fundamental unit in the corresponding ring and torsion points of the Jacobian?
How to get sum of points on the Jacobian (maybe the Mumford algorithm).

I want to understand it as quickly as I can, so I want to read a clear monograph. It would be great if that monograph (book or some lecture notes or survey or something) requires minimal possible background.
Thanks for any references.

REPLY [2 votes]: An elementary introduction to hyperelliptic curves by Menezes, Wu and Zuccherato gives a good elementary overview, especially if you want to understand the arithmetic on Jacobians.
If you would like to go a bit deeper into the topic, Part A of the book Diophantine Geometry: An Introduction by Hindry and Silverman is very useful if you want to understand the geometry of these objects better. The chapter is titled The Geometry of Curves and Abelian Varieties. I found it really useful, it was not an easy reference to find and I wish I knew about this book earlier.