Lamentations of the Flame Princess, subtitled Weird Fantasy Role-Playing, is a dark fantasy RPG in the "old-school" vein. That means that it shares many characteristics with the first edition of Dungeons & Dragons.
It is a class and level based system with races modeled as character classes. A character's attributes are determined randomly. They give modifiers to various other stats and actions (hit point bonus, damage bonus, armor class bonus, etc.). Hit points of a character are also rolled up and depend on his class and level. Every character has also five different saving throws against various hazards (magic, poison, area effects, etc.). The last important characteristics are the attack bonus and the armor class.
Attacks in combat are rolled on a d20. The character adds his attack bonus and needs to score higher than his opponent's armor class. A successful hit deals damage equal to the weapons damage rating which is subtracted from the opponents hit points. The game allows for some variant tactics like defensive fighting, parrying, aiming, mounted combat, etc.
There are some common skills for adventuring activities like hunting, stealth, or climbing. Most of these activities have a basic chance to succeed on a d6. This chance is the same for all character classes. Only the "specialist" class gets points per level to increase the chances.
Characters that use magic are granted a fixed number of spells per level that they can cast. The spells only refresh after a period of several hours of rest.