My aim in this paper is a modest one. I wish to describe in concise terms the structure of transcendental phenomenology and its principal application as a universal theory of science.¹ I believe that the terms in which I describe transcendental phenomenology are amenable to doing phenomenology. I shall furthermore discuss the problem of the foundations of mathematics from the viewpoint of phenomenology and I shall apply phenomenological analysis to the problem of distinguishing between mathematics and the empirical sciences as well as to the problem of giving a characterization of the nature of mathematics.