Abstract: "Triangular geometry" is the study of tensor-triangular structures, as they appear in several different areas of mathematics: Algebraic Geometry, Modular Representation Theory, Homotopy Theory, Motivic Theory, Noncommutative Geometry, etc. I'll introduce the notion of "spectrum", which is the key to the unified theory. The motto is then to develop geometric ideas, inspired by some of the examples, in this new abstract framework and then to apply them back in the various fields where the spectrum is sufficiently well understood.