The point, line, plane, and solid objects represent the first three dimensions, but a kind of reversal of space is involved in the ascent to a fourth dimension. Steiner leads us to this new perspective with words, diagrams, analogies, and examples of many kinds. In doing so, he continues his life-long project of demonstrating that our objective, everyday thinking is the lowest rung of a ladder that reaches up to literally infinite heights. Translated into English (from GA 324a) for the first time, these talks and the other selections on many mathematical topics bring us to tantalizing new horizons of awareness. They discuss: -- The relationship between geometric studies and developing direct perception of spiritual realities-- Constructing a fourth-dimensional hypercube-- Creating dimensions through movement-- Six dimensions of the self-aware human being-- The relationship of the Trinity and the angelic hierarchies to physical space