Cassels J.V.S. An Introduction to the Geometry of Numbers

New York: Springer, 1996. — 357 p.Notation
Prologue
LatticesBases and sublattices
Lattices under linear transformation
Forms and lattices
The polar lattice
ReductionThe basic process
Definite quadratic forms
Indefinite quadratic forms
Binary cubic forms
Other forms
Theorems of BLICHFELDT and MINKOWSKIBLICHFELDT'S and MINKOWSKI's theorems
Generalisations to non-negative functions
Characterisation of lattices
Lattice constants
A method of MORDELL
Representation of integers by quadratic forms
Distance-FunctionsGeneral distance-functions
Convex sets
Distance-functions and lattices
MAHLER'S compactness theoremLinear transformations
Convergence of lattices
Compactness for lattices
Critical lattices
Bounded star-bodies
Reducibility
Convex bodies
Spheres
Applications to diophantine approximation
The theorem of MINKOWSKI-HLAWKASublattices of prime index
The Minkowski-Hlawka Theorem
SCHMIDT's theorems
A conjecture of Rogers
Unbounded star-bodies
The quotient spaceGeneral properties
The sum theorem
Successive minimaSpheres
General distance-functions
Convex sets
Polar convex bodies
Packingsets with V(S) = 2^n ⊿(S)
VORONOï's results
Preparatory lemmas
FEJES TÓTH's theorem
Cylinders
Packing of spheres
The product of n linear forms
AutomorphsSpecial forms
A method of Mordell
Existence of automorphs
Isolation theorems
Applications of isolation
An infinity of solutions
Local methods
Inhomogeneous problemsConvex sets
Transference theorems for convex sets
Product of n linear forms
Appendix