Reference request - Lattices for studying number fields

Question

I am working on number fields and I have just started studying ideal class group. I came across with the Minkowski's convex body theorem, which simply says: $$ \text{Let } L \text{ be a lattice in } \mathbb{R^d} \text{ and } K \text{ - a convex set symmetric w.r. to 0} $$

$$ \text{If } \lambda(K) \geq 2^d\text{Vol}(L) \text{, then } K \text{ has a non zero lattice point} .$$

I have only basic knowledge on lattices. To understand the theorem, I looked for some books, notes but they do not have the definition of the volume of a lattice or quotient lattices etc.

There are few reference request questions on the site but as I mentioned, they do not help me with the algebraic number theoretical arguments like the theorem above.

So, can you suggest me some references to understand what is going on, please?

Answer 1

See chapter IV of Algebraic Number Theory by Pierre Samuel, available at Dover.