I'm installing a fresh Debian Linux right now and I was wondering what's the advantage of formatting disks with LVM instead of normal partitions?
Unless you're building a large, multi-disk platform on Linux (e.g. hosting server farm), there's really no use for LVM. If you're installing Linux on desktop you're most likely to not need LVM.
LVM is useful for example for adding new disks that count towards the diskspace available on the same logical partition, so that server users get more disk space without the need of adding new partitions. That's basically it.