Formula score theory (FST) associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating ability distributions from sequences of item responses can be reformulated as maximizing a convex index of goodness of fit defined on a convex set. A major simplification of several theoretical problems has been obtained because the linear mathematics used by the theory has a well-developed generalization to problems involving many variables. For example, a battery of tests measuring several related variables and one test measuring one trait can be analyzed with essentially the same theory. An elementary outline of the basic theory is presented along with a discussion of several illustrative applications. (Author)