Jung is said to have striven to rid himself of uncriticized assumptions although he asserted that a fundamental hypothesis is necessary. (I don't think he did this--witness his racist and sexist remarks as pointed out in Naomi Goldenberg's Changing of the Gods). To Jung the goal was "true expression" which consists in giving form to whatever is observed. The concepts of Jung's analytical psychology are not considered to be explanatory constructs by means of naming recurring experiences. He use traditional names whenever possible to indicate the "warp and woof of the mind in all its amazing complexity." (This acceptance of traditional names hardly involves critical reflections upon society's assumptions).
He is said to have found the modern movement towards quantification and causal theoretical explanations to be inadequate for psychological tasks. Statistical knowledge allows generalized statements of humanity, but offers little understanding of individuality. For self-knowledge a person must understand the unique individual facts, whose regularity is illuminated very little by theoretical assumptions or generalized knowledge (but he came up with his own typology). Jung claimed that in order to understand one must put aside all prejudice (yet he was unable to truly do this himself).
In order to do justice to his call for an appreciation of individuality, Jung added several concepts to his conceptual system that are said to be remarkable on the context of traditional psychological theories. For instance, he emphasized the teleological importance of purpose and meaning, especially in regard to normal, non-pathological phenomena. To Jung psychic process are not just the rest of past forces still living in the present, but also show spontaneous movement towards goals in the future. Only by answering the question of purpose, he thinks, can we come to an understanding of it meaning. Just as one could speak of causality, Jung brought forth the notion of synchronicity to refer to events that occur simultaneously and are meaningful but not causally connected, as in the case of much parapsychological phenomenon.
Another second aspect of humanity he points out is the human capacity of myth-making. Events and experiences that are deep, penetrating, and meaningful tend to be appropriated in our fantasy world to help make up our story, or myth, of ourselves. Each of these events or experiences refer to some type of felt absolute in each individual's life. Thus the myths we make give meaning to human existence and helps us in coming to terms with the world that lies both within and without the self. Unfortunately the increasing role of reason in our world has made it difficult for us to participate in the mythical process. To Jung, the more we mythologize, the more of the unconscious we make available to the conscious, and the more we integrate aspects of our lives. Thus it has become, according to Jung, the task of psychology to help humanity in this process of integration (this is true for people like Jung, such a method of therapy for differently directed persons may be very detrimental, it may also reflect more a theological assumption than a psychological truth.)
JUNG'S UNDERSTANDING OF THE PSYCHE:
The archetypes, Jung thought, are not memories of past experiences but "forms without content" representing the possibility of a certain type of perception and action. They offer a certain kind of readiness to produce the same or similar mythical ideas over and over again. To Jung they are "the ruling powers, the gods, images of the dominant laws and principles, and of typical, regularly occurring events in the soul's cycle of experience." They are responsible for the human quality of human beings, are on the effects and deposits of experience but are also active agents that cause the repetition of these same experiences.
Because we can only know of the manifestations of the archetypes--historical and individual--we can say very little about them. Jung speculates that there are as many archetypes as there are typical persons and situations in human experience. Because a fluid interpenetration is part of their nature, however, they cannot be clearly circumscribed or reduced to a formula. Thus to Jung reductive explanation is neither desirable nor possible.
From years of psychiatric work and phenomenological research in religions and mythologies, Jung identified several key motifs that the archetypes can take. The ones that he felt were especially important include: the persona, the shadow, the anima/animus, the mother, the child, the wise old man, and the self. To Jung, abstract figures, situations, places and processes can also give expression to them.
THE PERSONA: is the mask we wear to make a particular impression on others; it may reveal and conceal our real nature. It is called an artificial personality that is a compromise between a person's real individuality and society's expectations--usually society's demands take precedence. It is made up of things like professional titles, roles, habits of social behaviour, etc. It serves to both guarantee social order and to protect the individual's private life. That is, when the ego identifies itself with the persona, the individual become particularly susceptible to the unconscious.
THE SHADOW: Is a step further towards self-realization when one recognizes and integrates it. It is the negative or inferior (undeveloped) side of the personality. It is said to be made up of all the reprehensible characteristics that each of us wish to deny, including animal tendencies that Jung claims we have inherited from our infra-human ancestors. It is said to coincide with the personal unconscious and because all of us has one it appears to be a collective phenomena.
The more unaware of the shadow we are, the blacker and denser it is. The more dissociated it is from conscious life, the more it will display a compensatory demonic dynamism. It is often projected outwards on individual or groups who are then thought to embody all the immature, evil, or repressed elements of the individual's own psyche. (Symbols of the devil and the serpent contain elements of the shadow).
ANIMA / ANIMUS: following a person's coming to term with their shadow they are then confronted with the problem of the anima/animus, the archetype which is said to personify the soul, or inner attitude. It is usually a persona and often takes on the characteristics of the opposite sex. The anima is said to represent the feminine in men, and come from three sources: 1] individual man's experience with women as companion;  man's own femininity--rooted presumably in the minority of female genes and hormones present in man's body; and  the inherited collective image that has been formed from man's collective experience of woman through out the centuries.
Anima often appears in dreams, as long as she remains unconscious. She may also be projected outwards onto various women--first the mother, then lover and wife as one grows. This projection is said to be responsible for the passionate attraction or aversion and a man's general apprehension of the nature of women. Should a man mistakenly identify with the anima, Jung says, she can produce effeminaty or homosexuality. The anima remains in an compensatory relationship with the outer, conscious attitude. The more a man identifies with the masculine persona, the more he will be subject to the projections of his anima. In all men the anima is responsible for moods and is a complication in all emotional relationships (rather a stereotypical statement, certainly reflects no attempt to remove himself from cultural assumptions).
After the middle of life, according to Jung, the anima is essential for vitality, flexibility and human kindness. She appears in a variety of manifestations which reflect her bipolarity. She can be both positive and negative from one moment to another, young and then old, mother and then lover, good and them evil, and so on. She is an ambivalent image and has occult connections with the ancient mysteries and hence a religious tinge.
The animus is the comparable counterpart in the female psyche. (Naomi Goldenberg's critique points out that Jung provides emperical evidence for anima, but the 'animus' is just a postulate opposite. See: Changing of the Gods and Returning Words to Flesh). It is said to be the woman's image of a man. Unlike the anima, the animus appears in a plurality of forms. To Jung this reflects the differences in male and female conscious attitudes. He says that the woman's consciousness tends to be exclusively personal and centred upon the family, the man is made up of various worlds of which the family is only one. Thus he finds the anima and animus to be the opposites of each of these conscious attitudes, plural and singular respectively. (Again we find stereotypes of male and female. The fact is that men are trained to be more sinle minded that are women in Western Society. Things have changed dramatically since the last century and the roles of men and women have altered drastically. Jung's response to women who work, unfortunately, is that work too much are too masculine and undesirable, if not suffering from pathology.)
For the anima Eros is the undifferentiated unconscious principle (the root of all emotions), for the animus it is logos (which in the woman's mind is said to be responsible for unreasoned opinion and critical disputatiousness). Animus manifests itself most often in words and not images (Emma Jung), typically as a voice that comments on a person's situation or imparts general rules. When it does take a form, usually in dreams, it appears as a "plurality of men, a group of fathers, a council, a court, or some gathering of wise men," etc. It may also manifest itself in the single figure of a real man--father, lover, brother, teacher, judge, sage, etc. It is in short a manifestation of a man distinguished in some way by mental capacities or other masculine qualities (since when is thinking a purely masculine quality?). Its positive forms are characteristically benevolent, knowledgeable or understanding; its negative aspects are cruelly demanding, violently tyrannical, seductive, moralistic or censorious. It can also function, like that anima, as a bridge between the inner and outer worlds.
THE MOTHER ARCHETYPE: range of images of mother archetype are almost inexhaustible--usually some from of maternal aspect, the underworld, womb-like, etc. Most important of this archetype is mothers of the literal sense followed by those of the figurative. It may also be symbolized in a variety of impersonal forms (paradise [of birth], Kingdom Of God, church, university, city or country, earth, woods, sea, moon, gardens, caves, cooking vessels, certain animals--cow, hare). Evil symbols include, in the Western context, dragons, witches, graves, deep water, and death.
THE CHILD ARCHETYPE: Also takes many forms--child, god, dwarf, hobbits, elf, animals--monkey--or objects: jewels, chalices or the golden ball (trickster like). It represents original or child like conditions in the life of the individual or the species, and thus reminds the conscious mind of its origins and helps to keep them continuous. A necessary reminder when the consciousness become too one sided, too willfully progressive in a manner that threatens the sever the individual from the roots of his or her being. It also signifies the potentiality of future personality development, it anticipates the synthesis of opposites and the attainment of wholeness. Thus it is said to represent the urge and compulsion towards self-realization. This is a reason that so many of the mythical saviour gods are childlike in their nature.
THE WISE OLD MAN: is the archetype of meaning or spirit. It often appears as grandfather, sage, magician, king, doctor, priest, professor, or any other authority figure. It represents insight, wisdom, cleverness, willingness to help, moral qualities. His appearance serves to warn of dangers, provide protective gifts and so one (Gandalf in Lord of the Rings). As with the other archetypes the wise old man also possesses both good and bad aspects.
THE SELF: this is, according to Jung, the most important archetype. It is called the "midpoint of the personality" a centre between consciousness and the unconsciousness. It signifies the harmony and balance between the various opposing qualities that make up the psyche. It remains basically incomprehensible, as ego consciousness cannot grasp this supraordinate personality of which the ego is only one element. The symbols of the self can be anything that the ego takes to be a greater totality than itself. Thus many symbols fall short of expressing the self in its fullest development. Symbols of the self are often manifested in geometrical forms (mandalas) or by the quaternity (Any figure with four parts). Prominent human figures which represent the self are the Buddha or Christ. This archetype is also represented by the divine child and by various pairs--father and son, king and queen, god and goddess, or by a hermaphrodite.
Theriomorphic symbols include powerful animals such as the dragon, the snake, elephant, lion, and bear, etc. It is also expressed by plants--lotus and rose--and various mythic objects--the holy grail, philosopher's stone. To Jung the self is a representation of the "god within us."
THE DYNAMICS OF SELF-REALIZATION--INDIVIDUATION:
To Jung individuation means becoming an in-dividual, it implies becoming one's own self. We could thus translate it as "self-realization." The aim of individuation is nothingness than to divest the self of the false wrappings of the persona and the suggestive power of the archetypes.
Individuation must not be confused with individualism, which over-looks collective factors and seeks some peculiarity valued by the ego. Although Jung calls individuation an "ineluctable (not to be avoided) psychological necessity" he also says that its nature is aristocratic, and that it is available only to individuals who are predisposed to attain a higher degree of consciousness and who are called to it from the beginning (elitism). To Jung the average person is content with limited horizons that do not include knowledge of the collective unconscious. (What does this mean? Is reading Jung enough? Must one go through a crisis?) Still he presumes that wider consciousness may be a universal capacity.
The transition from this first stage to the next occur, says Jung, between 35-40. Along with it is supposed to come an urgent need to re-examine accepted values and to appreciate the opposites of earlier ideals. This stage is marked by Introversion where a person's concerns progressively become centred in the internal world and the fuller development of the psyche. This is a time of culture and wisdom and is governed by its own principles which are directed toward the end of self-realization through the union of opposites.
A further pair of basic types that Jung outlines are those of sensation and intuition. These are two differing modes of apprehension. Sensation refers to the process of perceiving physical stimuli from both outward events and inwards organic changes. Its opposite is intuition: which is said to mediate perceptions in an unconscious way. Intuition yields a content that is said to be whole and complete, a knowledge that possesses immediate certainty and conviction (Kant's a priori). Both sensation and intuition are called irrational as they deliver perceptions which are not based upon reason.
The next pairs of types that Jung points out is concerned with the conceptual relationships of psychic contents. He divides the means of doing this into thinking and feeling. Active thinking is directed and undertaken intentionally toward the end of some judgment. Passive thinking is called intuitive and is a case in which conceptual connections seem to establish themselves of their own accord and may lead to judgments that are contrary to one's intention. Both of these forms of thinking are to be distinguished from associative thinking, which produces ideas that form no connections and yield no judgments. Jung, it must be noted, considers only directed thinking to be rational, as the undirected thinking lies in unconscious processes and the idea of associative thinking is not really thinking at all.
Thinking is viewed as an opposite to feeling. It is a process that responds to psychic content with a subjective judgment of values. It is considered rational insofar as it is influenced by reflection and is in accord with the laws of reason.
The ideal situation to Jung is one in which the individual develops equally each of the two attitudes of extroversion and introversion, as well as the four functions of sensation and intuition, thinking and feeling, and also the two modes of apprehension, perceiving and judging. Every one, however, is considered to prefer one or the other opposites that from these pairs. One of the three sets of pairs ailing themselves to the person's aspect of extroversion or introversion. When one function is singled out it becomes superior and remains in conscious behavioral patterns, while the other, less favoured opposites, falls into unconsciousness--called the inferior function--here it remains inaccessible, undifferentiated and autonomous (but not dormant). The remaining two functions become secondary and operate in the service of the superior function.