It happens that I stumbled on a class of infinite dimensional Lie algebras that are not Kac-Moody algebras and for which I was not really prepared for. I know some general results on infinite dimensional Lie algebras from Kac's first two chapters of his book. Is there any more comprehensive and up to date reference?

If possible I'm interested in an approach to Lie algebras similar to the one of Kac (starting from Chevalley-Serre relations) and something not in the line of those suggested in this answer ( References: Infinite dimensional Lie algebras )