@wnj - I have been enjoying πΆππππππ₯ π΄ππππππ ππππππ‘πππ by Herbert Lange and Christina Birkenhake - not easy, but full of beautiful material. Complex abelian varieties are the 'best' complex tori. The same authors have an earlier book πΆππππππ₯ ππππ, but for some stupid reason I haven't looked at that yet.