Reality is Absolute
Reality is that which exists. It is absolute.
It is the standard of the true, the false, and the arbitrary.
Things are what they are, independent of our or anyone else's feelings, ideas, wishes, desires, and emotions.
Or, in the immortal words of Aristotle: A is A. To be, is to be something: finite, limited, and non-contradictory.

Reason is man's means of survival
Reason is man's only means of knowing reality, upon which his survival in reality depends.
Whether man is alone on a desert island, scurrying around with a pack of savages, or living in a city of billions: man must think -- and then act on his thinking, if life is his goal.

The individual is sovereign
Man is a rational animal, and reality dictates that to survive, man must be rational -- by choice.Man is a being of free will. Man can choose to think, drift, or evade -- but choose he must. His thoughts determine: his character, his values, his emotions, and his actions, and so his thoughts determine his destiny.
As reason is solely the attribute of an individual, and man's thinking determines his choices and actions, then each man is the master of his own destiny. The individual sovereign.

Man is an end in himself, and not a slave to the ends of 'society'.
Man can gain immense values from living with other men in society -- namely knowledge and trade -- if it is a human society.
A human society is one in which each man holds as an absolute: that every man is an end in himself, and that other men are not his pawns, nor is he theirs.Or, in the words of John Galt,
"I swear -- by my life and by my love of it -- that I will never live for the sake of another man, nor ask another man to live for mine."
Such is the credo of the rational egoist -- the independent mind -- who recognizes no authority higher than his own judgment of the truth. Such a moralist recognizes that man's life is the standard of value -- that which supports man's life is the good, and that which destroys his life is the evil.
Individualism is not opposed to man living in society. Individualism is opposed to man living in society as a slave.

To live in society man needs rights
To live rationally in society, man requires only one thing from his fellow men: freedom of action. Freedom of action does not mean freedom to act by permission, which may be revoked at a dictator's, or a democratic mob's, whim, but the freedom to act as an absolute -- by right.
Man requires rights to those actions necessary to support his own life, the most fundamental right being the right to life, from which all other rights, including the right to liberty, property, and the pursuit of happiness, derive

Rights are moral principles...
Rights are moral principles defining a man's freedom of action in a social context.Rights are inalienable -- they may not be morally infringed upon, i.e., a thief may rob you, but morally he is in the wrong, and you are in the right.
Rights are not guarantees to things, but only guarantees to freedom of action (right to liberty) -- and a guarantee to the results of those actions (right to property).The only obligation one's rights impose on others is for them to leave you alone, i.e. free to act within your sphere of rights.