"Fear is the main source of superstition, and one of the main sources of cruelty. To conquer fear is the beginning of wisdom." -Bertrand Russell

What is fear? Fear only comes to that self which is attached or identified - specifically, with thoughts, emotions, or objects, confusing them for the supreme, indivisible Self. The most common fear is of that which is unknown: ideas that are taboo or seemingly strange, the night-time, winter, and especially our own unconscious. It is interesting to note that the word 'Hell' comes from a word meaning 'to cover or conceal,' which reminds us that the real Hell is our own, unintegrated self which reveals itself in our fears and weaknesses.

The seventh line of Liber Librae informs us "Thou therefore who desirest Magical Gifts, be sure that thy soul is firm and steadfast; for it is by flattering thy weaknesses that the Weak Ones will gain power over thee. Humble thyself before thy Self, yet fear neither man nor spirit. Fear is failure, and the forerunner of failure: and courage is the beginning of virtue."
When one is not wholly equilibrated & integrated, one's weaknesses can cause one to "fall." The weaker parts of ourselves are those things which are still unbalanced and liable to have attachment. Liber Librae tells us to "humble thyself," a lowercase self, "before thy Self" with an uppercase: The self which is connected to the senses (Nephesh) and ego/thoughts (Ruach) is subject to suffering, therefore we must humble it before the supreme Self, which is, according to the Atma Upanishad, "ever pure, indivisible, and uncompounded, far beyond the senses and the ego." This self is, Qabalistically, the Monad in Kether, or the Supernal Triangle above the abyss which is the last frontier for the ego. Liber Librae continues to tell us that we should fear nothing, "neither man nor spirit," which echoes a line from Liber AL vel Legis mentioned below. In the most forceful part of the line, Librae says simply that "Fear is failure" and that it is "the forerunner of failure." What quality should one cultivate to conquer fear? Courage - symbolized by the triumphant hawk of Horus. A certain courage is needed to go beyond attachments and delve without fear into the black womb of Night.

“We need a tremendous amount of energy and we dissipate it through fear but when there is this energy which comes from throwing off every form of fear, that energy itself produces the radical inward revolution... So you are left with yourself, and that is the actual state for a man to be who is very serious about all this; and as you are no longer looking to anybody or anything for help, you are already free to discover. And when there is freedom, there is energy; and when there is freedom it can never do anything wrong… a mind that has no fear is capable of great love. And when there is love it can do what it will.”
-Jiddu Krishnamurti, Freedom from the Known

Liber Librae, line 15 continues with the theme of fear: "Nevertheless have the greatest self-respect, and to that end sin not against thyself. The sin which is unpardonable is knowingly and wilfully to reject truth, to fear knowledge lest that knowledge pander not to thy prejudices."
To sin against oneself is to restrict oneself - in this case, to a certain ideology. Attachments to one's beliefs or dogma creates the possibility of fear when confronted with knowledge that does not "pander... to thy prejudices." In this way, Liber Librae advocates being open to all knowledge and never condemning it, especially "knowingly and willfully" which is a conscious repression of a part of oneself which is not integrated & balanced.

"The one permanent emotion of the inferior man is fear - fear of the unknown, the complex, the inexplicable. What he wants above everything else is safety." -Henry Louis Mencken

Liber AL vel Legis mentions fear in a few places. One place is in Chapter II, lines 46-47, where Hadit says, "Dost thou fail? Art thou sorry? Is fear in thine heart?Where I am these are not."
Crowley says in his New Commentary for this line "If one have a right apprehension of the Universe, if he know himself free, immortal, boundless, infinite force and fire, then may he will and dare. Fear, sorrow and failure are but phantoms." Failing implies that one can fail- in a sense, that one can 'die,' but Horus brings us the Aeon of the Crowned & Conquering Child (each one of us) who fears no death but knows himself/herself to be eternal. To be sorry is to live in regret - it affirms division in the Will & implies attachment to the temporal. To have fear is to forget oneself as "free, immortal, boundless;" fear also implies duality - a fear of something other than oneself infringing on oneself. Sister Mary Tricky once said, "Fear is faith that it won't work out." Hadit knows it will work out, for he is beyond time, senses, and the ego. Hadit is not where there is failure, sorrow, or fear (which is the forerunner to failure); perhaps he resides where there is no duality like the supreme Self who is "far beyond the senses and the ego" and he who, "in him all conflicts and expectations cease" (Atma Upanishad).

"Many of our fears are tissue-paper-thin, and a single courageous step would carry us clear through them." -Brendan Francis

One explicit line about fear appears in Chapter III, line 17, "Fear not at all; fear neither men nor Fates, nor gods, nor anything. Money fear not, nor laughter of the folk folly, nor any other power in heaven or upon the earth or under the earth. Nu is your refuge as Hadit your light; and I am the strength, force, vigour, of your arms."
This explicitly states to fear nothing - I doubt in the mystical sense of Nothing since she is "your refuge." This echoes Liber Librae and a quote by Marie Curie - "Nothing in life is to be feared. It is only to be understood (Binah)." This line is explained further in Crowley's Old Comment to this line: "The infinite unity is our refuge, since if our consciousness by in that unity, we shall care nothing for the friction of its component parts. And our light is the inmost point of illuminated consciousness." This echoes the Atma Upanishad once again which states "in him (Hadit) all conflicts and expectations cease." In the "highest" sense, Hadit is one with Nuit, there is no difference - just as Atman is one with Brahman according to the advaita tradition; perhaps, in both of these there is not a Unity but a complete Emptiness (Anatta) since both Hadit and Nuit are identified with 0 (Naught) anyways.

"Fear is static that prevents me from hearing myself." -Samuel Butler

In Liber LXV, Chapter I lines 45-46, it says: "Go thou unto the outermost places and subdue all things. Subdue thy fear and thy disgust. Then - yield!"
The "outermost places" are the deepest recesses of one's unconsciousness or Hell; to go to the outermost places and subdue all things means that all things would be part of oneself. One must subdue fear (attachment to ego or identity) and disgust (attachment to cultural, relative morality or dogma) to overcome all things and have no division between oneself and another part of oneself or the Universe.

"The moment you fear, you are nobody. It is fear that is the greatest cause of misery in the world. It is fear that is the greatest of all superstitions. It is fear that is the cause of our woes, and it is fearlessness that brings heaven in a moment."
-Swami Vivekananda

To summarize - fear, failure, and sorrow are all interconnected in that their existence implies duality...also duality implies their existence. To divest oneself of fear, one needs "courage" - to discard oneself of temporal attachments and to see oneself as the supreme Self of Hadit or Atman who is one with Nuit or Brahman. This oneness must be experienced to completely eliminate fear, perhaps in Samadhi.

"He who fears something gives it power over him." -Moorish Proverb