Question: Does anyone know a good book about lattices (as subgroups of a vector space $V$)?

Answer: 
[These notes of mine on geometry of numbers](http://alpha.math.uga.edu/%7Epete/geometryofnumbers.pdf) begin with a section on lattices in Euclidean space. However they are a work in progress and certainly not yet fully satisfactory. Of the references I myself have been consulting for this material, the one I have found most helpful with regard to basic material on lattices is [C.L. Siegel's *Lectures on the Geometry of Numbers*](http://books.google.com/books/about/Lectures_on_the_Geometry_of_Numbers.html?id=VA2W-dl78UYC).
Check the following:

Roman,Steven: "Lattices and Ordered Sets", Springer

Blyth, T.S.: "Lattices and Ordered Algebraic Structures" , Springer

Roggenkamp, Klaus - Huber-Dyson, Verena : "Lattices over Orders" , Springer