Utilitarian is an ethical system for political philosophy. It was invented by Jeremy Bentham and John Stuart Mill. Its primary direction is for the greatest good for the greatest number of citizens. Obviously there has been much development and theory concerning that. Utilitarianism may exist within nearly any form of modern government.
Libertarianism is a political outlook companion of a laissez faire kind of national and international political economy where people are free to determine their own actions so far as possible. It is less than pure anarchy, and is generally unrealistic so far as governing a modern society goes.
Egalitarianism is a political situation where people are generally on an equal social, political and financial track, and with upward, downward and lateral social mobility normal for all classes. It is not quite a classless society yet does not have hard social stratification either.