Below is a tentative list of topics.

The mathematical basics behind lattices: 

- covolume of a lattice

- Minkowski first and second theorems

- primitive vectors and primitive sublattices

- Minkowski and Korkine-Zolotarev reduction of a lattice. 

- Harder-Narasimhan filtration

- Space of lattices, Mahler compactness criterion, linear action, Haar measure

More advanced Mathematical topics:

- Hecke correspondence

- Siegel summation formula

- Application to shortest vector problem

- Rogers formula, applications to shortest vector problem

- covering radius.

Computational Complexity 

- Classical computational problems on lattices

- The LLL algorithm

- Worst-case to average-case reductions

Applications to Cryptography

- Hashing and Encryption

- The Learning with Errors Problem

- Computing over Encrypted Data