I will give a survey of the theory of (ordinary) Lakshmibai-Seshadri path model, due to P. Littelmann, for highest weight modules over Kac-Moody algebras;
an excellent reference is: Chapitre 8 of Prof. Kashiwara's book "Bases cristallines des groupes quantiques, SMF, 2002".
The plan of my lecture is as follows:
(0) Standard notation for Kac-Moody algebras
(1) Definition of Lakshmibai-Seshadri (LS) paths and some of their basic properties
(2) Definition of root operators on LS paths and some of their basic properties
(3) Combinatorial character formula of Weyl-Kac type (in terms of LS paths) for highest weight modules
(4) Tensor products and concatenations of LS paths
(5) Kashiwara's isomorphism theorem between crystal bases of highest weight modules and (ordinary) LS paths