The book is built to carry a single thought, which Schopenhauer says cannot be shortened without losing it. He sets it out in four books that examine one and the same world from two sides, each side viewed twice: the world as idea and the world as will, first in their ordinary aspect and then in their deeper one. This page characterizes the whole argument from Volume 1 of the Haldane and Kemp translation, which contains all four books.
The First Book treats the world as idea, or representation. Its opening claim is that the world is my idea: nothing is known except as an object for a subject, so space, time, and causality are forms the knowing mind brings to experience rather than features of things in themselves. Taken alone this view is true but one-sided, and Schopenhauer admits an inward reluctance to accept that the world is merely appearance. That reluctance points beyond it.
The Second Book turns to the world as will. The opening into the inner side of things is the body. I do not only watch my body move; I know its acts directly, from within, as will. Schopenhauer generalizes this: the inner reality of every appearance, from gravity and growth to animal instinct and human striving, is one undivided Will, blind and without final goal. This Will is the thing-in-itself, and the visible world in all its grades is its objectification.
The Third Book returns to the world as idea, now in a higher aspect. Above the endless chain of particular things stand the Platonic Ideas, the unchanging archetypes that are the Will's most direct grades of objectification. In aesthetic contemplation the mind can rise out of personal willing and grasp these Ideas, becoming for a time a pure, will-less, painless subject of knowledge. Art communicates this vision. Music holds a special place: it is not a copy of the Ideas but a copy of the Will itself, which is why it moves us so directly.
The Fourth Book treats the world as will once more, now as conduct and value. Because all willing springs from want, existence is shot through with suffering, and ordinary life swings between pain and boredom. Schopenhauer locates the root of virtue in compassion, in seeing through the illusion of separateness expressed by the Hindu formula 'this thou art.' Beyond justice and loving-kindness lies the final step: the denial of the will to live, the resignation reached by saints and ascetics and sometimes forced on ordinary people by great suffering. Philosophy can only interpret this; it cannot command it.